"just as well"?

I man you totally can radiate excess heat energy on earth, but your comment implies that the parents idea of radiating off excess "energy", specifically HEAT energy in space is possible, which it isn't.

You can radiate excess energy for sure, but you'd first have to convert it away from heat energy into light or radio waves or similar.

I don't think we even have that tech at this point in time, and neither do we have any concepts how this could be done in theory.