Technically yes, due to the extreme distances between particles in space we'd average a volume and say "negative temperature!".
However.
Those individual particles are shooting at extreme speed and momentum, so they're individually very hot.
And due to the lack of particles bouncing around in a given volume of space, you can't use conduction/convection (aka, here fellow particles, take some of my energy). Instead you can only use radiative cooling, which is crazy inefficient. For example, the ISS has 75KW of cooling across 1000 square meters.