Space is cold. There are just very little cold molecules to take over the energy from your hot molecules.
Here on earth we are surrounded by many molecules, that are not so cold, but colder than us and together they can take a lot of our excess heat energy away.
This prompted my curiosity. None of the following contradicts the thrust of your message, but I thought the nuance is interesting to share.
Interstellar space isn't a vacuum. Space is mostly empty compared to Earthly standards, but it still contains gas (mostly hydrogen and helium), dust, radiation, magnetic fields, and quantum activity.
The emptiest regions are incredibly sparse, but not completely empty. Even in a perfect vacuum, quantum mechanics predicst that particle-antiparticle pairs constantly pop in and out of existence, so empty space can be said to be buzzing with tiny fluctuations.
> Space is not cold. It has no real value for temperature. Stuff in space does.
The cosmic microwave background radiation, the left-over energy from the Big Bang, sets a baseline temperature of about 2.7K (-270°C), just above absolute zero.
Temperature depends on particle collisions, and since space isn't a vacuum, just incredibly sparse, one can talk about the temperature of space, but you're right that what is typically more relevant is the temperature of "specific" objects.
