It really depends - you can do direct injection to GEO now with cryogenic stages. And IIRC Soviets did some tests with kerolox stage (that should eventually launch on the ill fated N1) around the Moon, meaning multi-day flight times with liquid oxygen on board.
If you do the thermal design right, possibly use a sun shade (space is a large thermos bottle after all) or even use active cooling to remove the little heat that gets through, then it should work just fine. :)
The heat shield probably provides some degree of insulation from the solar radiation as well, and it's only needed on one side if you're far from Earth.
