In your AC unit in your house, there's something called a radiator, which is essentially a long pipe that is packed together into coils. There are usually two of these. Coolant travels through these coils and a fan blows on it to provide cold air to your house. In a similar but opposite way, in space you can have a lot lot lot lot more than just two radiators and fans would blow heat generated by the data center away to these coils to dissipate heat. The advantage of space is exactly that. Huge amount of space in all directions that allows you to have extremely massive amounts of tightly packed radiators. Whoever said space is cold is not right. Space isn't cold but it depends on how far you are from the sun. Relatively speaking, Earth is far enough that it would feel chill, like you're in a northern winter environment without any wind. Wind or air blowing on ice/cool air is what makes things cold. There's no wind in space.

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Data center in space equals free solar power and no need to pay huge sums for AC.

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