Technically interplanetary space is a hot plasma too. The particles emitted by the Sun are very hot according to kinetic theory (which only depends on the mean

Technically interplanetary space is a hot plasma too. The particles emitted by the Sun are very hot according to kinetic theory (which only depends on the mean velocity of particles) since they have a lot of energy. It's a plasma because the particles are charged and accelerated by the Sun's magnetic field. Of course the density of these particles is very low, so if your definition of heat factors those in then space is cold.