Most other instruments (NIRCam, NIRSpec, FGS/NIRISS) operate at about 40 Kelvin (-233°C) using only passive cooling (i.e. the sunshield).
Clearly this would be cold enough for a data center. Clearly the sunshield can be very well thermally insulated from the rest of the telescopy. The sun-facing side is up to 300°C hot. The cold side is -233°C.
I'm not saying radiating the heat from the GPUs is a solved problem. Just the thermal insulation between the solar panels and the rest of the spacecraft.
Putting an AI rack there is a completely different scale of power and cooling than what JWST uses.
(For simplicity assume the side facing the earth is full reflective)
That is converted to 2.5kW electic and 10.5kW heat. The electric is then used to power the computer and ply doom or whatever. That 2.5kW of electric is then converted to 2.5kW of heat. That means the satelite has to dissipate 13kW of heat.
But even without the electric use it still receives 13kW of heat and dissipates 13kW of heat.
Any object in space will emit as much energy via radiation as it receives otherwise it will continue to increase in temperature. The question is thus what temperature does it sit at to make this in equilibrium.
If the satelite was perfectly flat it would run at 120c for a black body. If it was a lump of stew it would be about 150c.
To reduce that to 20C you need about 50sqm radistor, or 5 times the surface area in shadow. The shadow is about 350-400m long
So you build it as a cone with the flat circular area facing the sun and the pointy area in its shadow you’d only need a cone height of about 20m to emit enough heat to keep the satelite to room temperature.