Not even remotely. For one thing, it's not even that cold out there; average temperature out at the main belt is only around -75 C, based on radiative equilibrium with the incoming sunlight. (Obviously, the near-earth asteroids are warmer.) And then you've got the problem that you're surrounded by vacuum, so the only way you have to dump heat for further cooling is through thermal radiation, which is terribly inefficient. Not to mention, thirdly, the fact that there's no natural helium available on asteroids, so you'd have to ship it up constantly to replace your coolant as it boiled off.
Meanwhile, here on Earth, we have billions of cubic feet of helium gas underground with infrastructure for liquefying it, we have access to conductive and convective cooling for our heat pumps with the whole thermal mass of the Earth to sink heat into, and we have all the industrial infrastructure and construction and maintenance infrastructure right here.
Oh, and if your datacenter is in Palo Alto instead of on Pallas, you have the added bonus that you don't have to worry about networking with a 15-minute ping.
tl;dr space isn't cold, vacuum isn't a great cooling medium, and shipping is expensive.
You'd have your radiators in the shade, where it's at least a hundred degrees cooler and you have the thermal mass of the asteroid where you can dump heat temporarily. Sourcing Helium might be difficult, but maybe you can get it from one of the gas giants?
That'd be even less efficient; the gas giants have much deeper gravity wells than Earth, and it's correspondingly much harder to bring material up from them. Jupiter's exhaust velocity is 60 km/s, Saturn's is 35 - compared to a measly 11 km/s for Earth. And as the rocket equation tells us, the fuel required goes up exponentially the greater the change in velocity you need.
This is easy to google (I should have done so before) but still hard to believe. If that's peak speed for only a short time because of fuel limits, it's less hard to believe.
...what do you mean by "peak speed for only a short time because of fuel limits?" It's space. You don't need fuel to maintain speed. What's going to slow you down?
Oh: To clarify, "Escape velocity" is the speed you need to escape Earth's gravity well entirely, so that you are no longer orbiting the Earth at all; it's about the amount of velocity you need to go on interplanetary missions. If you just want to go to, say, the Moon, then you don't need to go that fast. If you just want to go to low Earth orbit (LEO), then orbital velocity's only around 7 km/s.
But that isn't "peak speed" or anything, that's just ... how fast you have to go to be in low Earth orbit. The International Space Station is traveling at 7.67 km/s right now.
Meanwhile, here on Earth, we have billions of cubic feet of helium gas underground with infrastructure for liquefying it, we have access to conductive and convective cooling for our heat pumps with the whole thermal mass of the Earth to sink heat into, and we have all the industrial infrastructure and construction and maintenance infrastructure right here.
Oh, and if your datacenter is in Palo Alto instead of on Pallas, you have the added bonus that you don't have to worry about networking with a 15-minute ping.
tl;dr space isn't cold, vacuum isn't a great cooling medium, and shipping is expensive.