We need to clarify a few things about heat, temperature, and vacuum.
Heat–in the statistical mechanics sense–is mass with random kinetic energy. Temperature is essentially an aggregate measure of the speed of that motion; a faster moving particle has a higher temperature. This may not make it feel “hot” however.
For instance, when the stiffled air on a still summer day feels “hot”, it’s because all of the gas molecules that make up air are bouncing back and forth in every which direction. The reason you feel warm–even when the ambient temperature is lower than your body temperature–is because you can’t reject heat from your own biological processes very well. When a breeze picks up, you can eliminate heat via convection, which is why it feels cool. When you sweat or pour cold water on your face, you lose heat via evaporation, and when you put your forehead against a cold piece of metal, you reject body heat via conduction. (The body’s ability to radiate away heat is very low, lacking, as we do, an efficient blackbody surface. Be thankful for this; good blackbody radiators are equally good blackbody absorbers.)
This random motion also occurs in liquids or solids, even though the molecules aren’t as free to move around. Because liquids and solids are much denser they feel (and are) much hotter–that is, they contain more energy–than gases at the same temperature. Some types of material, particularly metals, also conduct heat very readily, while others like ceramics tend to localize heat. Why this happens is complicated and requires delving into solid state physics, but it’s along similar lines to why some substances are good electrical conductors and others insulate well, and as a general rule, substances that conduct electricity well are also good conductors of heat and vice versa, though this isn’t universally true.
Space, and by this I assume you mean the vacuum of space, strictly speaking has no temperature at all insofar as it is made up of no matter to store kinetic energy. And because it lacks mass to serve as a conduit for the conduction or convection of heat energy, it tends to isolate heat sources pretty well unless they’re either very good radiators or they can cool themselves via evaporation of their own mass. Now, there is the cosmic microwave background which fills the universe with radiation at a blackbody distribution peaking at around 160GHz and giving the night sky an effective blackbody temperature of around 2.7 Kelvin. What this means is that from the perspective of the second law of thermodynamics, the cosmic background can act as an essentially infinite heat sink at 2.7K, which is cold enough to radiate heat to from virtuallly any body. Where did this CMB radiation come from? It’s an echo from the time shortly after when the nascent expanding universe first became transparent to electromagnetic radiation at ~10[sup]13[/sup] seconds. Before this, everything was packed so close together in a plasma of baryonic matter and extremely short wavelength photons that light had essentially no free mean path. As the universe expanded, the background “temperature”–that is, the mean energy density and wavelength–decreased, even though the actual photons are still moving, as they always do, at c.
Space isn’t cold; it’s just mostly…nothing. And nothing can’t conduct, convect, or absorb energy. A major problem with designing spacecraft is to reject enough heat to keep it functional, or in the case of a manned craft, livable. This is why the Space Shuttle always flies in orbit with the cargo bay doors open and facing away from the Sun as much as possible; the radiators are mounted to the inner surfaces of the doors.
Stranger