Climate change is going to be a real problem in the future according to Michio Kaku in his book Physics of the Future and the source of the problem will be computers and the heat they produce.
No. I've never read the book, but I guarantee that you're misrepresenting what Kaku is saying, because the idea that the heat emitted from computers themselves would cause climate change (rather than the emissions from producing the electricity driving them in the first place) is legitimately crazy.
Furthermore if the heat convection of computers themselves are the problem, then reclaiming that heat for a useful purpose like described is pointless to solving this supposed problem, from a thermodynamic perspective, because you've still introduced that same amount of heat into the system.
The environmental benefit of such a setup obviously comes from a reduction in the amount of energy used specifically for heating in the first place by repurposing the heat emitted from devices that you would've been running anyway. That takes the whole thing back to energy generation being causative. So how on earth can that sentence make any sense at all?