I don't think this is true. It is not only power consumption but also power backup. If you can use smaller diesel engines and smaller battery packs this will lower the cost.
And why do you think datacenters have been raising temperatures? It saves a ton of money: https://www.datacenterknowledge.com/archives/2008/10/14/goog... HP estimated they saved 8 million. That is not a rounding error.
A server that uses less power will also generate less heat.
I have to admit it is years ago I worked for a company owning datacenters but at that time the highest costs were always: power and connectivity.