That's not necessarily a problem. Or at least it's a solvable problem. A surface greenhouse would be insulated. It would still lose heat to thermal radiation.

That's not necessarily a problem. Or at least it's a solvable problem. A surface greenhouse would be insulated. It would still lose heat to thermal radiation. I'm not sure of the rate. It may be manageable because when the Sun is shining, not only are you heating up but the plants themselves generate heat (ie it's a greenhouse). This may be another reason why you're better off growing plants underground because it lessens the temperature extremes. Otherwise things can be heated with waste heat or directly if required.