The heat has to go somewhere and that is the environment. 300 MWh is enough energy to boil over 3k metric tons of water. That's 107 medium fuel trucks for perspective.

Luckily AI data centers produce nowhere near that amount of heat. Remember the heat is waste and 300 MWh is the total draw. Some of that energy becomes heat. That ratio is somewhere like 100:1 though. Also, the waste water is only like 10F hotter than the intake. We build GW sized PP all the time and they will leak far more heat (as like on the order of 100x) than a 300 MWh AI data center. Thought there were supposed to be engineers on this site.

300 MW hr is approximately nothing to the broader environment. A constant gigawatt load is (off the top of my head, probably off a bit) something like 5 sq km of solar over a 24 hour period on average. Granted some of that light would otherwise be reflected but that gets us in the rough ballpark.

In local terms its a fair bit of heating but zooming out it's a drop in the bucket.

Yeah it gets radiated into space