The thermal gradient in space is meaningless because there is hardly any matter to dump the energy into. This means you are entirely reliant on thermal radiation. If you look at the numbers given by Stefan-Boltzmann law you'd see that means to radiate a significant amount of energy you need a combination of a lot of surface area and high temperatures.

This means you need some sort of heat pump. For a practical example you can look at the ISS, which has what they call the "External Active Thermal Control System" (EATCS), it's a complicated system and it provides 70kW of heat rejection. A datacenter in space would need to massively scale up such a system in order to cool itself.