As cool as space can be, it can also be incredibly hot. It's not uncommon to see huge temperature variations on the same object based on whether or not the surface in question is pointing toward or away from the sun. In any case, as others have said, there is no conduction or convection in space - only radiation, which needs a little help some times.
For an example, when I worked on the Hubble, a thermal short was discovered that would severely limit the life of one of the cameras, which have to be very cold to operate. In order to counteract that, a pretty complex cooling system was built to counteract the effect. It consisted of a couple of large metal boxes (a couple hundred pounds each, if I recall) attached to a couple of huge radiator panels. (About 3'x10' each, if memory serves). The whole thing took over a year to build and took a lot of care to launch and install.
And extremely hot (100C + in near-earth orbit) in the sun, and -273 in the shade - with nothing to conduct heat away - meaning that you can only emit heat as EM radiation (photons).
In a sense, yes. But space has no medium to convey heat so you can't get rid of it by convection or diffusion. Getting rid of heat in space is hard and a big issue for spacecrafts.
For an example, when I worked on the Hubble, a thermal short was discovered that would severely limit the life of one of the cameras, which have to be very cold to operate. In order to counteract that, a pretty complex cooling system was built to counteract the effect. It consisted of a couple of large metal boxes (a couple hundred pounds each, if I recall) attached to a couple of huge radiator panels. (About 3'x10' each, if memory serves). The whole thing took over a year to build and took a lot of care to launch and install.