Technology

I think you have to look at the actual orders of magnitude difference in raising the temperature of water versus air. The Arizona story you linked is about a study that found up to +4°F (+2.2°C) temperatures in air.

The same amount of heat, spread across the same volume of water moving at the same speeds, would only raise that water by ~~1/830 as much, for a +0.0048°F (+0.0027°C)~~ 1/3300 as much, for a +0.0012°F/+0.00067°C temperature change across the same area/volume.

~~(I got to 830 by taking the specific heat of dry air of approx 1 J/g K at room temperature and regular atmospheric pressure and 1.22 kg/m^3, versus water's 4.184 J/g K and 1000 kg/m^3).~~

(Edit: I fucked my math. Water has approximately 3300 times the heat capacity as air, per unit volume, and I just looked it up directly).

The higher conductivity of water might be offset by the higher convection potential of air (because air responds to temperature changes with differences in density/pressure, which creates wind in itself), so that the heat will spread through either medium relatively quickly and therefore dissipate very quickly with distance to the source.

I just don't see a world where a data center raises the water by even 1°C, even locally.