The most perfect place in the world to mine for bitcoins might just be Antarctica. Why? Because it has 2 elements in abundance needed to mine for bitcoins - a never-ending supply of freezing cold air, and endless wind due to the vast expanses of land with no trees or anything to break up the wind.
You also get ~6 months of continuous daylight.
To take advantage of the freezing cold outside, use liquid cooling throughout all your rigs and have it all funneled to radiators outside the building (or just build your rigs in a shed outside - probably an easier method, though it would suck to have to go out there all the time). The only problem I'd foresee would be if there was an interruption in your electricity supply from the wind turbines and you had your radiators for the cooling loops outside the water would freeze in the radiators - very very bad. So it would be best for those of your moving down south to mine for BTC to instead just place your PCs in a shed outside the outpost.
You would still need a lot of humidification and air conditioning. Antarctica is a desert, and you don't want to go around computers with that level of RH. Also, you would need a lot of batteries to maintain your environmental controls, unless you could somehow get permission to drill into the soil for use as a heat reservoir.
Now if you were lucky enough to secure a spot in an outpost there AND had somewhat limitless funds you could theoretically ship all the hardware you'd need to the base, and assemble it all. For electricity you could build small wind turbines. For internet just use 2-way satellite! And every once-in-a-while just buy more stuff off Newegg and have it shipped to your location.
I think you'd have to go through Raytheon for all of that. Maybe not...
Or you could just mine in space. Even in earth orbit it gets several hundred below zero.
You would have some serious problems with the feature sizes on the chips compared to the particles they're going to be getting hit with, unless you find a way to lift an enormous amount of shielding to your station/with your satellite.