What's the avarage temperature of the Universe?

It depends on how you want to average:

If you average by volume then all you need to think about is the bath of photons from the cosmic microwave background, at about 2.7 kelvin.

If you average by observable mass then the primary constituent is sparse atomic (H) and molecular (H₂) gas in the voids between galaxies – at a temperature of a few 10s of kelvin. Only about 1/10th of that mass is in stars, but their temperatures are far higher – closer to $10^4 {-} 10^5$ kelvin – so once you average that, you'll get something more like $10^3 {-} 10^4$ kelvin.

Finally, if you average by total mass – predominantly Dark Matter which is in virial equilibrium in most galactic halos, then the temperature would be way up to about $10^7$ kelvin.

The Universe is not in thermal equilibrium, so you cannot actually speak of current temperature. But "Earlier than a few 100,000 years the matter was ionized and a state of thermal equilibrium existed; at about this time the temperature was about 3000 K and the equilibrium ionization fraction of matter became very small. The Universe is said to have “recombined;” since neutral matter is transparent to the radiation, the CBR photons we detect today last scattered a few 100,000 years after the bang. After last scattering, the expansion simply red shifted the energy of CBR photons and diluted their number density, and, because of a remarkable feature of the expansion, a Planck distribution was maintained with a temperature that decreased in proportion to the size of the Universe. For this reason, the Universe today is filled with thermal radiation of temperature 2.726 K despite the fact that the Universe is no longer in thermal equilibrium." (http://arxiv.org/pdf/astro-ph/9308018)

You can measure the temperature by looking at the spectrum, and in this case you see a peak at 2.73 K. There are about $10^8$ times more CMB photons than starlight photons in the Universe at the present epoch.