Cooling a large nuclear power reactor would be a challenge on Mars. Probably you'd want something compact that runs at high temperature, like a molten salt design, to make heat rejection easier.
Edit: side benefit would be you could use the heat directly for processes like this metallurgy thing.
Cooling is should not be an issue, considering it goes to ~-80C at night, we only need a smart way of harnessing that difference.
No, it absolutely will be an issue. You need to dispose of ~100 MW of heat energy. Simply dumping it into ground will quickly heat it up, you can't rely on water evaporation for obvious reasons, same goes for convection because of the thin atmosphere. So your only option is radiative cooling, either by using ground or dedicated radiators. But because it's relatively inefficient, you will need a lot of area and materials for it.
High-temperature reactor designs are essential. Radiative heat transfer scales with temperature to the fourth power.
So if you reject 100 MW of waste heat at, say, 400°C (750°F), a radiative heat transfer area of 10,000 m^2 (i.e. 100m x 100m square) would be sufficient. That's quite big and hot, but 100 MW is a lot!
Radiative heat rejection at 100°C would require 10x as much area.
Disposing heat at a higher temperature would also mean that you need to dispose of more heat (~2x in the case of 400°C vs sub-100°C) and losing energy which could've been used for useful work such as generating electricity.
It may be reasonable to do at early stages, but after the colony is able to produce metals in situ it would be better to build more radiators. Especially considering that you also need to dispose latent heat from other sources.
...which is why you would want to fabricate as many of those radiators as possible on site, with local materials. And also why one of the key requirements for space base nuclear reactors is "scalable".
Mars atmosphere is so thin that it won't really help to cool down a reactor.