The short answer is that ~100m2 of steel plate at 1400C (just below its melting point) will shed 50MW of power in black body radiation.
I would assume such a setup involves multiple stages of heat pumps to from GPU to 1400C radiatoe. Obviously that's going to impact efficiency.
Also I'm not seriously suggesting that 1400C radiators is a reasonable approach to cooling a space data centre. It's just intended to demonstrate how infeasible the idea is.
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.
Moreover, a heat pump would add an equipment with moving parts that can fail, requiring maintenance.