Come on, dude:
Already addressed.
There is currently a kilopower project on paper and testing for providing power to an early Mars colony that would NOT have the necessary water resource for cooling. Heat can be radiated off or converted to electric. Depending on how much heat we are talking about.
You remember that Curiosity tiny nuclear reactor? It has a dedicated radiator for radiating. There is a picture of those radiator and some stat. It generate 2,000 watt of thermal power and 150 watt of electric power. Heck it doesn't use all of that thermal/heat for electric and instead use some of it to keep itself warm. Mars night are pretty darn colder than reasonable.
https://mars.nasa.gov/files/mep/MMRTG_Jan2008.pdf
In space all spacecraft (no matter what their design are) will always need some sort of heat source (either from power source or moving heat from different part of hull that are warmer). Because if a certain part of their spacecraft remain in dark all the time, It would get to -250 F degree. Converse being in sun can go as much + 250 F degree.
I would like to add something to the topic of heat handling. I recently install a new CPU which was a huge upgrade and also generate even more heat than my older CPU.
My older CPU was an phenom II 1075T which did generate a bit of heat. But is pretty darn slow relative to modern CPU and never had problem with a smaller heat air cooler. I have been using that one CPU for more than 3 years. I moved over to AMD Ryzen 1700X. Oh boy it does generate heat like nobody business! I have a liquid cooler to handle that heat. It barely hit 100 F degree while browsing the internet.
The funny part is my GPU is actually running way more hot than my CPU.
Anyway back to topic of heat handling. All I have to say is liquid are great for cooling.
All this heat talking has remind me of something that you can look into. ISS has 10 radiators for heat dissipating (ETCS and PVTCS) and they use liquid ammonia to move heat around. Because radiator work by having lot of surface area to radiate heat. You can scale the system to handle larger load by making larger radiator or add more radiator.
https://space.stackexchange.com/questions/3702/does-the-iss-need-more-heating-or-more-cooling
In additional you can also turn off things that aren't mission critical to reduce heat generation to allow radiator to handle larger load from reactor or vice versa.
TD;LR: Not impossible to handle larger heat load in space.