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Compared to the temperatures encountered in lunar nights, the desired operating temperature of the James Webb Space Telescope is very low. Lunar nights are typically -170°C while the operating temperature of JWST is -220°C.

If surviving lunar nights are difficult to ensure the survival of the electronics, say on lunar rovers, in the low temperatures, then how does JWST overcome this issue?
And why not make use of the same methods adopted in JWST onboard the lunar rovers to survive lunar nights, sans the notorious nuclear heating?

From Status of the JWST Sunshield and Spacecraft found in @Antzi
's answer:

Most of the electronics is on the "hot side" but there needs to be some conventional electronics on the cold side (beside the cooled IR sensor chips).

Small thermal environments on the cold side are equipped with heaters to provide mini-environments at normal operating temperature for these electronic devices.

[...]Thermostatically control heaters are used to
maintain equipment above minimum required temperature while under cold conditions. Heater drive electronics (HDE) controlled heaters are used to maintain the +J3 panel, propulsion lines, battery, star tracker, and 1 Hz isolators within the required stability range.

The spacecraft component temperatures are maintained within the required limits by the use of radiators, heat pipes, MLI, and heaters. Thermostat and software controlled heaters are the two types used on this spacecraft. The software control heaters are used to maintain tight temperature control for critical spacecraft components and structures. The heaters are controlled by flight software with temperature feedback control. The flight software enables the ground to modify any TCS mission constants which include on/off heater set-points and failure thresholds.

If surviving lunar nights are difficult to ensure the survival of the electronics, say on lunar rovers, in the low temperatures,

The temperature itself is not the primary reason.

Lunar nights are difficult to survive because you have 14 days of darkness. If you want to design a solar-powered rover that can store enough energy to stay warm for 14 days, the rover becomes large and heavy. Too heavy to launch with current rockets.

So we use nuclear decay heaters instead, which are much smaller and lighter.

The alternative is to power down for the lunar night. But then the entire rover cools down, and will heat up again the next morning. These heat cycles are the usual cause of death: because different materials expand and contract at different rates, it's really difficult to design electronics that stay intact with such large temperature swings.

JWST, on the other hand, is in permanent sunlight. This has several consequences:

• you can heat the electronics directly by putting them on the hot side of the spacecraft


• you can use electric power from the solar panels to run heaters on the cold side, without needing large batteries.

So you can't use the methods from JWST on a lunar rover: their environments are too different.

Nuclear heating isn't "notorious", it just makes the mission a bit more expensive. It's a mature, reliable technology that works, so why not use it?