Amazon have a scheme like that in the Town land of Tallaght close to where I live. Sadly district heating is not common or popular in Ireland so most of it many data centres just exhaust the waste heat.https://www.sdcc.ie/en/news/tallaght-district-heating-network-and-energy-centre-officially-opened.html
 

I’m guessing that data centers don’t generate enough heat to then turn the heat into electricity again via a turbine or any other method? It seems like an opportunity. Since it seems like we are continuing to accelerate the concentration of wealth we really could use good solutions to help those who aren’t on the winning side. Although it seems clear to me that there is going to be a large global shift in the next couple of decades so maybe a lot things will change. The 1920s were turbulent and so are the 2020s. Maybe we are in a simulation ;)
 

That would be more complicated, as the heat is below the boiling point of water. You'd first need a heat pump to "concentrate" the energy, before being able to use a steam turbine. Theoretically possible, but probably not very efficient.
 

The perpetuum mobile has been disproven quite a while ago! Unfortunately thermo couplings (direct heat to electricity) have a very low return and are only used in very specific circumstances (like the spaceprobes Voyager).