Assume your datacenter runs at 50C (122F) and the temperature outside is -40C (-40F), using the datacenter heat to generate electricity has theoretical maximum efficiency of 27.85%. If your datacenter is at 23C (73F) and room temp is 0C (32F), then the theoretical maximum is 7.77%. Note the word 'theoretical maximum', in reality probably at least 10 times worse than that.
Newer generations of CPUs are going to be exchange less frequently but will produce more energy as they offer more dense computing. This makes case for investing more in the server hardware.
Even then understand, that 7% of a huge amount of energy is still huge amount of energy.
Edit: Apparently "Facebook datacenter in Denmark is supplying around 10.000 homes with heating" -- source, another poster.
So... you need to rethink your expertise on defining what is and what is not viable.
But alas, it has to be said.
No, you can't create perpetuum mobile ie. build a machine that given a supply of energy produces as much or even more energy.
https://en.wikipedia.org/wiki/Perpetuum_mobile