Comment by adrian_b

The temperature of space datacenters will be limited to 100 Celsius degrees, because otherwise the electronic equipment will be destroyed.

So your huge metal plate would radiate (1673/374)^4 = 400 times less heat, i.e. only 125 kW.

In reality, it would radiate much less than that, even if made of copper or silver covered with Vantablack, because the limited thermal conductivity will reduce the temperature for the parts distant from the body.