Something smells wrong. You could dump a gigawatt into resistive heating and not see such temperature rises so far away.
Then there is also the heat island effect. Concrete boxes will heat up an area more than dirt or wood, even if those boxes are completely empty inside. If you build them near where people live, people are gonna notice. Houses have gardens, industrial complexes such as data centers and factories don't.
Also, the effect is more concentrated downwind, so the heat effect is not some kind of uniform distribution in all directions.
If you had a hypothetical 1 GW generator and used a hypothetical 1 GW loadbank with 1 GW of resistive heating and a fan that was outdoors, the air temperature would rise.