A data center is never going to rely on just passive heat transfer through walls in its operation. It will need active ventilation and a lot of it. Depending on climate and location, it will probably need active cooling at least part of the year. If you were in a cool dry climate, you could figure out how to do it with passive cooling and that would be neat. Alternatively you could build the whole room out of copper with finned walls (like a big baseboard radiator) to radically increase the surface area. This still wouldn’t work, but it would look cool.
Cheers,
Eric