Space is cold, but there's not much there, so your flux will be very small. Of the three ways to move heat (radiation, convection, and conduction) you're basically reduced to radiation, which is the least efficient.
cold of space? Unfortunately, no - space is an extremely effective insulator, so it's extremely difficult to get rid of heat. You need large heat sinks (which adds weight) and they have piss-poor efficiency in space. So your cold side would get hot very quickly