I’m confused. Rejecting one GW of heat to the building exterior with heat exchangers is going to heat up the area around the heat exchangers.
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.
The air temperature would rise near the heat source, and that hot air would rise in a plume and disperse, not seep out laterally.