The answer really depends on what you mean by vacuum. If you mean what’s left when all the atoms etc are pumped out, then it'll have a temperature of electromagnetic radiation.

Temperature of the vacuum

It is possible to use the zeroth law definition of temperature to assign a temperature to something not normally associated with temperatures, like a perfect vacuum. Because all objects emit black body radiation, a thermometer in a vacuum away from thermally radiating sources will radiate away its own thermal energy; decreasing in temperature indefinitely until it reaches the zero-point energy limit. At that point it can be said to be in equilibrium with the vacuum and by definition at the same temperature. A gas that behaved ideally all the way down to absolute zero, obeying the kinetic theory of gases, would achieve zero kinetic energy per particle, and thereby achieve absolute zero temperature. Thus, by the zeroth law a perfect, isolated vacuum is at absolute zero temperature. Note that in order to behave ideally in this context it is necessary for the atoms of the gas to have no zero point energy. It will turn out not to matter that this is not possible because the second law definition of temperature will yield the same result for any unique vacuum state.

More realistically, no such ideal vacuum exists. For instance a thermometer in a vacuum chamber which is maintained at some finite temperature (say, chamber is in the lab at room temperature) will equilibrate with the thermal radiation it receives from the chamber and with time reaches the temperature of the chamber. If a thermometer orbiting the Earth is exposed to sunlight, then it equilibrates at the temperature at which power received by the thermometer from the Sun is exactly equal to the power radiated away by thermal radiation of the thermometer. For a black body this equilibrium temperature is about 281 K (+8 °C). Since Earth has an albedo of 30%, average temperature as seen from space is lower than for a black body, 254 K, while the surface temperature is considerably higher due to the greenhouse effect.

A thermometer isolated from solar radiation (in the shade of the Earth, for example) is still exposed to thermal radiation of Earth - thus will show some equilibrium temperature at which it receives and radiates equal amount of energy. If this thermometer is close to Earth then its equilibrium temperature is about 236 K (-37 °C) provided that Earth surface is at 281 K.

A thermometer far away from the Solar system still receives Cosmic microwave background radiation. Equilibrium temperature of such thermometer is about 2.725 K, which is the temperature of a photon gas constituting black body microwave background radiation at present state of expansion of Universe. This temperature is sometimes referred to as the temperature of space. This temperature is thus like a test charge in that it facilitates a measure of the system even though temperature is not strictly defined there.Temperature of the vacuum

hiiii

A thermometer "in a vacuum" will be in thermal equilibrium with the
electromagnetic radiation field surrounding it. You cannot get away from this
even if the thermometer is in outer space. It will equilibrate with the
radiation field to which it is exposed (not just visible but from the
longest wavelength microwave through X-rays and gamma rays. This mode of
energy exchange occurs even in a "perfect vacuum" since it requires no
medium to transport the energy. So the thermometer will record the average
energy field. Of course you have to generalize what you mean by the
"thermometer". A typical mercury in glass type may not be appropriate for
the measurement.



temperature is a property of matter (it is related to how much energy is
stored in the mater in the form of motion -- vibrations) and hence does
not apply to a vacuum.

Heat can be transferred by conduction, convection, or radiation.  By
putting the thermometer in a (perfect) vacuum you have removed the
opportunities for conduction and convection.  Radiation is the only path
for energy transfer and hence temperature change.  If the surroundings
of the vacuum container are cooler than the thermometer it will loose
energy to its surroundings by radiation -- though very slowly   !!!!!