The interstellar universe is a vacuum, how can it have a temperature? And why do we see light but not feel it?

Answer

In the first instance, the term ‘temperature’ only has meaning when we can speak of thermodynamic equilibrium. This means that on a microscopic scale, the particles interact with each other so often that an equilibrium is established in which the energy is ‘democratically’ distributed, according to the laws of statistics. The temperature is then a measure of the average energy of the particles.

You are right to question the tenuous environment between the stars in that context. There the few particles hardly interact with each other, so there is no thermodynamic equilibrium. Anyway, that interstellar center is not completely empty, and every particle has its energy, and there is an average of it. The interstellar center strives for balance, but never achieves it, simply because it takes longer to reach that balance than new events disrupt the balance. To a certain extent, the ideal gas law still applies. If the pressure is about the same everywhere, this means that the temperature is highest where there is least matter.

I suspect your question has to do with news about what is called the cosmic microwave background radiation, the so-called afterglow of the Big Bang. That early universe was both energetic and dense. Then the particles interacted enough with each other to achieve the same uniform temperature. A hot gas emits radiation, according to a spectrum well defined by physics. A universe that used to be dense and hot therefore contained such radiation. After expansion, the radiation cools, and it persists even when the atoms and the radiation barely interact with each other. We now see that radiation, and we call its temperature, the temperature of the universe. But the radiation hardly interacts with the thin gas between the stars, indeed.

As for ‘feeling’. We do feel electromagnetic radiation, it interacts with our skin. You do feel that you are standing in the sun. But the cosmological radiation of the universe carries little energy per photon, so we don’t feel it.