Yeah, maybe not impossible, but I mean extremely unlikely. I found a thread on reddit that had examples and a spreadsheet https://www.reddit.com/r/IsaacArthur/comments/11kp7s4/how_large_of_a_heatradiator_would_a_spacecraft/

To run a data center in space you would need some kind of reactor producing around 100 MW. If rejecting 100 MW at 800 K

A= 100,000,000 / 0.85×5.670374419e−8×800

The number is the Stefan-Boltzmann constant (σ) https://physics.knox.edu/OnlineHW/zTest-PhysicalConstants.html

A≈5,065 m²

So roughly:

5,100 m² of radiating surface

That is a square about:

√(5065) ≈71 m per side

If it is a double-sided radiator panel, the physical panel area could be about half:

2,530 m² of panel, about 50 m × 50 m, assuming both sides radiate effectively.

Also temperature matters enormously so

At emissivity 0.85:

So the answer is about 5,000 m² (lol this is like “a football field” on each side) at 800 K, but balloons to absurd levels like hundreds of thousands of m² if you are trying to dump room-temperature waste heat which there would be a significant amount of. That is for a single small data center at current power needs. In the US alone data centers use 176 TWh (https://www.congress.gov/crs-product/R48646), so there is no chance we are going to be migrating a significant portion of it into space.