Thermodynamics
doesn't work like that.
I could write a long post about heat transfer through matters of all sorts (basically the thermal conductivity of the wall of the space ship would be the key to determining the outside temperature of the surface in complete vacuum), but for experimental confirmation, go and see if your house's outside walls are at room temperature during wintertime. If they are, I recommend investing in something called insulation.
Space ships have good insulation because they do not want to waste energy into something like heating when they can get that as a side effect of running any devices, and in most cases space ships need to spend energy on actively cooling the ship instead.
Basically, every spaceship (like everything else, duh) needs to be in thermal equilibrium in order to not freeze or overheat. That means it needs to radiate the same amount of energy as it is receiving from the outside, plus all the excess heat that the systems are producing.
The amount of energy received depends largely on how close to a sun the ship is. For reference, Moon's surface can reach up to 107 degrees celcius during daytime, although Moon's albedo is not exactly the best of all materials. Suffice to say that on the lit side, ship surfaces are hot, on the dark side they are cold, and this has far more relevance to surface temperature than anything that is within the ship. This is not exactly a problem, since every object in space finds it's thermal equilibrium and therefore it would not exactly make it any easier or harder to separate a ship from, say, an asteroid of similar size.
The problem for space ships and stealth comes from excess heat produced by the ship's systems and appliances, and that is the only thing that can basically separate a ship from any lump of rock as far as detection goes.
However, the excess heat usually is transferred away via radiators that radiate the energy into space. Alternatively, the excess heat can be stored in heat sinks when running at stealth mode, sort of like submarines go into silent mode when trying to specifically avoid detection by passive sensors.
And even when using radiators, the ship can simply turn so that the radiators are on the non-visible side to potential observers.
The fact is, there are ways to minimize the EM signature for a limited period of time. Even completely neutralize it, should the need arise, for a while. Simply turn everything off, put a sweater on and use glowsticks for lighting and emergency oxygen supply for breathing.
Radar signature can be masked likewise - just make the ship's surface indistinguishable (via radar signal analysis) from an asteroid.