Trivia

If an object has no molecules, the concept of temperature is meaningless. That's why it's technically incorrect to speak of the "cold of outer space" — space has no temperature, and is known as a "temperature sink," meaning it drains heat out of things.

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Yes, it would be really cold. Temperature measures the energy per "degree of freedom" (i.e. way something can move) of whatever molecules happen to be around. So, it it becomes so cold that the molecules stop all together, then this is the "absolute zero" temperature. On the Celsius Temperature Scale (i.e. water freezes at 0, and boils at 100) this takes place at -273 degrees C. We usually use the Kelvin temperature scale, where Zero Kelvin is this "absolute zero" temperature -- or -273 degrees C. Water freezes at +273 Kelvin and water boils at +373 Kelvin.

If we put a thermometer in darkest space, with absolutely nothing around, it would first have to cool off. This might take a very very long time. Once it cooled off, it would read 2.7 Kelvin. This is because of the "3 degree microwave background radiation." No matter where you go, you cannot escape it -- it is always there.