There's very little on JWST that makes it hot. Furthermore, the spacecraft bus where the non-scientific instruments exist) is on the other side of the sunshade so that the waste heat from the RAD750 (a single processor clocked at 118 MHz - PowerPC 750 architecture (Macintosh computers in '97) that uses 5 watts of power designed to operate -55°C to 125°C) doesn't interfere with the scientific instruments.

Putting an AI rack there is a completely different scale of power and cooling than what JWST uses.