Temperature is a measurement of the average motion of particles in a given volume. Space is a vacuum which means there’s very few particles in a given volume. Even if all of the particles in a given region of space have maximum movement the average across the volume is extremely low because the density of the particles is so low.
It’s not really that space is cold. It’s that space is empty and it cannot have temperature if it is empty.
Additionally, if you could instantly transport yourself into space right now and didn’t have to worry about breathing, you wouldn’t feel cold at all. You will actually overheat because the lack of particles would mean that the heat generated by your body would have almost nowhere to go.
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