I gotta say, I think that this would do nothing but increase the efficiency of electricity generation. If it becomes more profitable to generate electricity for your mining purposes by installing your own solar array, or your own hydroelectric, wind, or tidal generating system, then that's what people will do, and in the Bitcoin 'arms race', that would almost guarantee that in order to remain profitable, EVERYBODY mining bitcoin would be required to convert to renewable energy, in order to remain competitive. And it's really not hard to scale up an installation economically. So if you have to put in a (arbitrarily picking a number here) $50,000 installation to run your farm, and it takes another $$3000-$5000 to go ahead and scale up enough to run the rest of your home, then it's safe to assume that most folks running a home-based operation large enough to justify continuing to mine (meaning they economically have no choice but to switch to renewable energy) would go ahead and do it up for their homes as well. Less residential consumption (although probably an insignificant impact, some is better than none, right? It's a start).
7% of the world's energy generation being shifted to renewable energy, essentially 'overnight' would have significant impact in areas that would 'trickle down'. Economies of scale in alternative energy production equipment would make it affordable for the average joe to now also invest in cheaper renewable energy (like solar or wind), for his home/business which would have a domino effect on the current constraints limiting people from switching (cost). People aren't burning oil and coal because they hate the environment, they're doing it because it's too expensive to shift. Implementation is currently so low that there's no economy of scale that allows producers to make energy production equipment cheap enough for the average consumer. Most people can't justify the upfront costs of spending $10,000-$20,000 for a solar system that is going to take 20 years to pay for itself (assuming no maintenance costs), and last for 30, just to save $75-$100/month on their electricity bill.
The bitcoin mining 'climate control' systems are also interesting to me.
As to the question regarding how heat from a mining farm could be converted to COOL a building, you might want to read up on "Absorbtion cooling" It's one of the most efficient methods for cooling, and the original way that refrigerators worked (propane or natural gas). Not a new concept, zero moving parts, so maintenance costs would be essentially ZERO. Not to mention, you could ALSO use the heat to heat water. Be that residential water, a pool, hot tub, what have you...
Sounds to me like if your theory is correct, we could potentially move a very large portion of our current energy consumption to renewable energy, move heating and cooling to a nearly 100% efficiency scale (turning "waste" heat into building heating/cooling), all while kicking the banksters and oligarchs to the curb.
Empty the banking buildings, move in huge mining farms, harvest the heat waste for climate control, and move in legitimate jobs in their place. Win/Win/Win.