Proof of cold can be used to at least mitigate if not eliminate the environmental cost and in fact to increase decentralization in a POW system. In a POW system if a use is found for the "waste" heat, and that use is only of value if decentralized, then the security of the network is still maintained. Proof of cold means putting the waste heat from proof of work to good use by displacing the energy otherwise used for space heating in cold climates. So for example a transaction in Melbourne, Australia where it is say 30C in January gets secured in Winnipeg, Canada where it is -30C in January.
Industrial mining appears to be concentrating in locations with the least expensive power and passive cooling. Increasingly, ASIC manufacturers are vertically integrating with industrial miners. The fact that mining equipment rapidly becomes obsolete means that an ASIC space heater will offset electrical heating costs for one season at most. Then the rig is simply not worth running at all, e.g. too noisy. I have three GPU mining rigs ready to heat my Colorado mountain home should GPU-algorithm coins ever again be profitable to mine, but I doubt that I will ever take them out of storage.
PoW secures a blockchain that only needs securing because anonymous, possibly malicious, peers compete. Conventional financial networks are secured at much less expense, and the block rewards of PoW coins should be better spent elsewhere.
It does not need to offset 100% of the heating cost even if it only offsets say 10% of the heating cost the the effective energy cost of securing the network is still actually zero. Furthermore the industrial miners have the same problem of obsolescence, and more importantly are still treating the heat produced as waste. This is frame of mind question. Rather than think of an ASIC that produces waste heat we think of a space heater that uses crypto-currency mining to offset part of its operational cost. As for the noise that is a design question. There are also many conventional space heaters that are noisy.