Average temperature on Mars is -60C. You won't need water for liquid cooling. Standard metal heat sinks would work fine at temps that low.
In a vacuum or near vacuum, that is just not correct.
https://letstalkscience.ca/educational-resources/backgrounde...
By the way, "air-cooled" does not mean the air cools the chips. In fact, the problem is that the air near the chips gets warm, because the air absorbs the heat and acts as a blanket. Air-cooled means you are pushing the hot air away from the chip and bringing in cooler air. But the absence of air means the problem (or solution, depending on context) never exists in the first place, it just dissipates.
The thinner the atmosphere, the easier to keep cool anything. You need air to retain heat, not to dissipate it. Right, without the Earth's atmosphere, we'd lose most of our heat at night, nearly all of it, and we'd have deep sub-zero temps every night even in the summer, even though we're closer to sun by a lot than Mars, we're still on the outskirts of the habitable zone for a planet.
And the only thing you can do is move the heat because of conservation of energy. There is no other way to get rid of it.