Waste heat from data centers can boost air temperatures in downwind neighborhoods by as much as 4 degrees Fahrenheit, researchers at Arizona State University report in a new study conducted in the Phoenix metro area, the hottest in the U.S.
and maybe to some degree, you can stick heat into groundwater
Do it long enough, and even that would become a problem. There are parts of the London Underground that are uncomfortably hot to ride because it’s existed so long they’ve managed to heat-soak the ground around the tunnels.
The heat in the tunnels is largely generated by the trains, with a small amount coming from station equipment and passengers. Around 79% is absorbed by the tunnels’ walls, 10% is removed by ventilation, and the other 11% remains in the tunnels.[3]
Temperatures on the Underground have slowly increased as the clay around the tunnels has warmed up; in the early days of the Underground it was advertised as a place to keep cool on hot days. However, over time the temperature has slowly risen as the heat sink formed by the clay has reached its thermal capacity. When the tunnels were built the clay temperature was around 14 °C (57 °F); this has now risen to 19–26 °C (66–79 °F) and air temperatures in the tunnels now reach as high as 30 °C (86 °F).[3][4][5]
Do it long enough, and even that would become a problem. There are parts of the London Underground that are uncomfortably hot to ride because it’s existed so long they’ve managed to heat-soak the ground around the tunnels.
That’s a neat tidbit.
https://en.wikipedia.org/wiki/London_Underground_cooling