Not sure if I follow really. Cooling from it's own generated heat? Are we even sure the system would get that hot in the first place? The temperatures can plunge up to -200 degrees.
If needed, they'd cool it just like they keep the James Webb Telescope cool.
>>deepan+(OP)
Keeping things cool in space is very hard. On earth we usually transfer heat from one medium to another (water to water, water to air, etc.). In space that's not possible because even though the matter in space is quite cold, there is very little. Therefore the only real way to get rid of heat in space is to radiate it away (think infrared light bulb). The James Webb Telescope does the same thing.
>>deepan+(OP)
The Webb telescope is a _wildly_ different apparatus, designed from the ground up to run as cool as possible, and with an effectively unlimited budget. It lives in the shadow of the Earth behind multiple layers of shielding. These "data centers" need to live in direct sunlight and operate as cheaply as possible _at scale._ Very little of Webb's tech is applicable.