Let's say there is an exoplanet orbiting its host star well outside its habitable zone. Suppose further that it has a lot of water, being perhaps comparable to earth when it comes to the volume ratio of water compared to the remainder of the planet.
Now water at its densest is 4° Celsius warm. My question is: Could the exoplanet's weight force the water into a liquid state by squeezing it to the temperature of lowest density?
My intuition would say no, because after all, temperature is nothing but molecular movement, and every kind of accelerated movement is supposed to lower the total energy of a system, which seems to be absurd.
Also, this seems to be an explanation of the so-called "faint young sun paradox", which is well-known in geology.
If the answer differs from that, I would be pleased to read an explanation of how my reasoning was flawed.