Mars
Some of the assumptions here are wrong. It is easier to dissipate heat in space then it is to in the earths atmosphere. The key is how it is done, you still want a radiator to do it, but the radiator is used to also heat the vessel as well as cool the engines, and also to give propulsion.
There are many designs for a nuclear engine. Here is an older NASA brief on one that you can look at by searching for 636883main_FDR_talk_NIAC_2012_final.pdf (Google it--NASA site).
Also, as for global warming... A solar minimum like this is exactly the opposite. Without the warming effects on the top of the atmosphere from the stronger solar storms and solar winds, this will lead to a cooling of the earth, such as the referenced mini ice age during the period this was thought to last happen. From my understanding, when the solar activity is at a minimum, the temperature of the sun (Outer Corona) is lower.