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Mount Kilimanjaro, despite being close to the Equator, has permanent glaciers on its top.

This hints toward the solution to your problem: orography!

While one hemisphere is mostly flat, with limited elevation and can enjoy the benefit of a warm climate, the other hemisphere is much more mountainous with most of its peaks above the snow line. The precipitation that one side would be tropical rain falls as snow on the mountains, and stay frozen because of the low temperatures.

Have the planet be half of a binary pair with the two tidally locked to each other but very close together (close to the Roche limit but not within it).

The two would orbit around the star and their mutual spin would provide a normal day-night cycle but the side towards the partner would receive less sunlight due to the shade from the other half of the binary and as a result would be colder.

Combine an significant axial tilt with a elliptical orbit.

Axial tilt allows one hemisphere to be in winter while the other is in summer. Earth has approximately 23.44 degrees of tilt. Even in mid-summer the temperature at the south pole is far from tropical because the sun never rises above 23 degrees and sunlight is correspondingly dim. 45 degrees is too much since the south pole would get twice as much sun as the equator (when south pole is pointed toward the sun). 30 degrees might be a good guess, the pole would get more sun than the equator at the peak of summer, but the equator would get more sun at other times.

Earth has a slightly eccentric orbit; it is nearly circular. Because of the duration of summer and winter is almost the same. Since Earth is closer to the sun (and moving faster) when it is winter in the northern hemisphere, the northern hemisphere has longer summers and the southern hemisphere has longer winters. In 2006, the northern hemisphere summer was 4.66 days longer than winter

Now, increase the eccentricity of Earth's orbit until the winter 6 times as long as the summer (in the colder southern hemisphere). Consider the northern hemisphere first, summer is now 5 times longer than the winter, but the solar radiance is not at high as on Earth because it is further away from the some (keeping the same orbital period), but first day of summer is not the hottest because of thermal inertia. The much longer summer would allow thermal inertia to create a much longer tropical conditions period than might otherwise be expected.

The southern hemisphere will be bitterly cold for months on end (during the dog days of the norther hemisphere).

Now, the northern hemisphere will endure a brief (about 1.5 month) winter, the would have have little sunlight and decidedly non-tropical. Thermal inertia will keep the temperatures from being too frigid.

I am assuming significant amount of ocean as a prerequisite for thermal inertia - because this gives a result more closely in line with the desired outcome. Without oceans, temperature change will be more intense (hotter summers, colder winters).

Due to precession, the winter / summer conditions will change over time, i.e., the northern hemisphere will experience the long winters, then thousands of years later it will experience short winters, and so as as the precession cycle repeats. 26,000 years in the case of Earth.

This won't precisely yield a planet with the conditions desired, but I think it is probably closer than you will get with other realistic conditions.

This is simply not possible unless you are willing to go for questionably odd planetary features

Messing with the axial tilt would be the closest you may get to your scenario in a clean way, but even the pole-equator climate switch will only get you a ring of moderate "tropics" around the equator and a seasonal switch from Hell to Helheim on the poles. I would recommend this as it is the least odd and most probable scenario.

However, there might be another way. If the sides have a significantly different albedo one could be cooler than the other. The following scenario is just one way to do this, artificial structures and terraforming gone wrong would also be good explanations. Imagine a planet, half solar-collector farm, and half nature preserve.

The Martian Way

Mars used to have a big ocean covering almost the entire northern hemisphere. Imagine this ocean, but covering half of both hemispheres. Now, this world is really cold. So cold that it mimics Earth during the Cryogenian Period and the ocean side nearly freezes over completely. The continent side, however, has a much higher albedo (the world will need some very dark rocks) and absorbs much more heat than the reflective frozen ocean side. This may allow for continent based zones with a microclimate fit for rainforests near the equator.

This won´t be a clean solution, the ice will probably have an equatorial "channel" and the "warm side will have a lot of tundra and glaciers. So not a tropical paradise on one side but covered in ice and glaciers on the opposite side but one frozen ocean side and one warmer tundra side with the planet's rainforests in equatorial retreats. If you make the tropical retreats geothermally active this could also aid the survival of the forest and create valleys with actually pleasant microclimate. I would furthermore suggest keeping the planets axial tilt low, so seasons don´t mess up the planets delicate climate setup.

Massive Geo-Engineering

1. Tilt the planet by 90°




2. Place a self-stabilizing sunshade at the L1 point




3. Place massive, controllable mirror-arrays at L3 and L4 and selectively heat the desired hemisphere and somehow manage the heat-transfer of the atmosphere

One way you could have an effect somewhat similar to what you describe is to have a planet with a variable axial tilt. Having for example the North hemisphere permanently tilted away from the sun would keep it in permanent winter, while the South would be in permanent summer. Where the variable part comes in is that the tilt itself would need to be "locked" in such a way that it shifts exactly with the rotation of the planet around its star so as to always keep the same pole tilted towards the sun. I will admit that this does seem highly improbable, however you could probably fit it into the story.

Have one hemisphere to have much higher terrain features than the other. The higher you go, the colder it gets due to atmospheric pressure.

That happens because for most gases, if you take a constant volume of them, temperature is proportional to pressure and mass.

Mars has the features you need. This is a rendition of what it would look like if you filled the lower plains with water:

If instead we kept the planet dry and pressurized it to have Esrth-like pressure at any point, the plateaus would be naturally colder than the lower lands.

This works with any rocky planet capavle of holding an atmosphere.

The planet is close to the galactic core, but far from plane.

Your systems plane happens to run parallel to the galactic plane while being fair close to the galactic core/center, the galactic core produces a lot of light. The large number of star on one side and the comparatively small number on the other means one hemisphere is receiving considerably more light, to the point its night would not be as dark as night in the other hemisphere. Keep in mind the light side is also going to receive a lot more radiation.

With some mechanism to prevent the atmospheres mixing, simple climate change on one hemisphere would not affect the other. For example, an equatorial bulge or chain of mountains high enough to prevent most of the weather from crossing. If you didn't need stability in geological scale, even weather structures could form a suitable barrier for hundreds or even thousands of years.

With a barrier between them, one hemisphere could be runaway greenhouse CO2-rich jungle (whether from volcanic action, cultural effects, differences in plant respiration, shortage of water, higher albedo, etc etc...) while the other is an icy wasteland.

The separation of the mountains would form a wall against the ice all too reminiscent of the wall in the Game of Thrones, though.

If the sun is the main source of contributions to global temperature then this is gonna be rather unfeasible because the planet spins.

So, instead you need to have a smaller star which produces much less light, and an internal source of heat that is more dominant on one side.

You can have a planet which has an extremely hot core which warms up the planet, but due to chance and a large asteroid impact in the distant past, has very different atmospheres on different sides of the planet. One side might have extremely active volcanoes which spew out a lot of chemicals that break down global warming gases, while the other might have volcanoes which spew out global warming gases.

As such, one side is hot and one side is cold. The hot side will remain hot, day and night, and the cold side will remain cold day and night.