Could shaping radiators differently help? Say, a curved radiator over the hull or so? I know 'skin' radiators existed for the Apollo Manned module, but what about for reactor and engines?
Yeah, but there's issues as was mentioned by others.
There IS a radiator design that partially mitigates it - rather than covering the hull in a radiator you cover it in a reflector and spray coolant right out into space down along parallel to the hull, to be caught and recycled at the bottom of the rocket. Compared with regular radiators it has the following benefits:
+ Rocket can stay well armored
+ Radiator is MUCH more resistant to damage and easier to armor
+ Weighs much less than a normal radiator
+ Has more surface area than a regular radiator covering the same area
+ Is more efficient than a regular radiator
And downsides:
- You lose coolant over time
- You especially lose coolant during maneuvers
- Higher coolant requirements eat into some of the other efficiency gains
- If you run out of coolant you're in trouble
- You lose efficiency from half the surface area you're radiating into being your own ship