Comment by amluto

Yes, absolutely, but it will depend on where one is, the surrounding geography, etc.

A hairdryer pointed at me from 1m away running 24/7 will make me notably warmer. A hairdryer 20m away is probably unnoticeable. A 1GW datacenter is a lot of hairdryers. At some scale, there is probably a buoyancy effect such that cooler air will be drawn in near the surface, get heated, and convect upwards, so I could even believe that a monster datacenter would cool some surrounding areas. (The sun inland from the west coast in the US has this effect during certain seasons, and AIUI this is a good part of the reason that the areas very near the coast tend to be dramatically cooler than inland areas in the spring and early summer.)