Computation doesn't destroy the energy. If your system is fed by a Sun-like star you still get a Sun-like excess in radiation. At 6 K or 1/1000 of the Sun's surface temperature you need 1000^4 times the surface area, or a radius of 0.07 light years. The system would show up as an absurdly bright (~20 times the background where we look for 0.001% deviations) and relatively big spot in CMB surveys. You can change the temperature but the result won't change, you can't hide a radiation excess that large close to us. Probably not even 0.001% of it.