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Wizards in fantasy worlds are very often portrayed in thick robes and hats (and of course long beards and hair for the men). These don't seem very practical for summers or any kind of hot weather (assuming wizards can't just have all their clothing enchanted with on-going air-conditioning effects.)

What is a realistic hot-weather outfit for a wizard, given their typical, particular needs (freedom of movement for casting, various books, potions, reagents, etc.)? Bonus points for example images and/or references to realistic/historical fashion.

Thinner robes? Seriously the broad brimmed hat is great for sunny weather or wet. If the robes are heavy wool they'll be almost water proof and plenty warm, thinner wool for cool spring and autumn weather and linsey-woolsey, a 50-50 blend of wool and the flax fibre used to make linen for the summer months in cooler climates, cotton, linen or silk according to local availability where it gets really hot in the summer. The Bedouin of the Sahara traditionally wear pale colored linen robes and head scarves to help them survive the desert heat. By sticking to a clothing pattern and varying only the materials wizards won't find themselves unexpectedly encumbered by a change in the weather.

The Gandalfesque wizard is a European wizard.

Robes make sense if you are in England. If you want a wizard from a hot climate, take a look at how people in that climate dressed historically when they wanted to put on a show and impress. These Javanese performers are not wizards (I don't think) but their outfits would be great for a hot climate wizard: lots of skin, lots of ornaments, creepy masks.

You can find wizards from anywhere. Googling around found Tahitians, Khmer, Indians; use search term sorcerer and you do better with African and pre-contact Americas. There is no shortage of amazing stuff for you to copy for your fiction.

Lots of desert people wear long robes; if the sun is punishing enough, you'll want to cover up even if you are quite dark skinned. Loose fitting airy robes help keep you cool in those sorts of conditions, and by way of a bonus stop you getting too cold too quick when the sun sets, as in deserts the nights are often cold.

I won't try and ramble on here; images are the only really interesting things, and a) I'm finding it hard to locate really nice images worth showing you (because I'm a bit rubbish at image searching) and b) really, the photos will show a bunch of people in robes in interesting places. You don't really need to see them to know that yes, robes can and do work in very hot desert areas, and have been used for that exact purpose for well over a thousand years.

"Freedom of movement for casting" is ill defined, but constricting clothing is absolutely not what you want in very hot weather, so that's ok.

If your wizards want robes, then they can have robes. No problem

Tuareg man. I think he's wearing cotton; certainly it appears to be quite a light fabric. More info on Tuareg clothing, plus links.

(as an unrelated footnote, Tuaregs are islamic but it is the men who wear the veils)

Bedouin Sheikh. Note the black robes; when the sun is hot enough, the colour of your clothing doesn't really matter that much. White won't save you. Traditional bedouin robes were woolen, too.

The idea that a wizard wears a long robe is, surprisingly, a pretty old one. It's not a modern fantasy stereotype.

At least since the time of a Roman toga there was an implicit connection between long loose clothing and the lack of necessity to fight or work for a living.

In the 10th century the whole Europe started adopting Byzantine fashions, and we see kings in loose long robes on the miniatures, while fighting men and peasants wear shorter tunics. The Church had also adopted Byzantine fashions, so both Catholic and Orthodox priests and monks even now wear clothes that didn't change much from 10th century.

Free townspeople of high standing and scholars wore long robes in 15th century too.

In 17-19th century all the manners of loose silk robes of Eastern origin were worn as a part of domestic clothing by gentlemen of leisure, philosophers and writers. This banyan is an ancestor of a modern dressing gown and a bathrobe.

So we can conclude that the idea that an older man who doesn't need to fight or engage in other physical activity, but rather spends his time reading, writing, studying, teaching and discussing with other similar gentlemen, will wear long loose clothes, is entrenched enough in European culture that it doesn't need a reality check.

As for the materials, there are several ways to approach it. If we position medieval and not modern approach to sweat and body odor, you can continue wearing wool in a lot of environments. Ancient Greek and Roman clothes were mainly wool - and it gets pretty hot in Mediterranean. As other answers write, Bedouin clothes were traditionally wool.

If you are not afraid of your own sweat, wool is pretty comfortable when hot - maybe because it's a material more or less similar to human hair, being made from animal hair :)

Other materials like silk and cotton are already covered in other answers.

About the only environment you don't won't to wear wool in is warm and hot tropical. Buddhist monks still manage to wear long loose clothes there, even though it's rather a wraparound thingie and not a tailored robe.

UPD: as far as carrying the gear is concerned, in a medieval-ish world a wizard shouldn't carry all his gear with books and potions on his person. Just like a knight wouldn't always wear his armor and weapons. A knight would have a packhorse and a squire. A high-ranking wizard will have a mule and an apprentice to take care of that for him.