The Universe is mostly empty space, with a few stars floating around. Steafan's suggested we take all the heat energy from all the suns, plus all the emptiness, and average it out. How cold would it end up being? The question sounds a bit unusual but there's a good reason to ask it; this is one of the ways Scientists think the Universe might end. It's called the "Heat death of the Universe" hypothesis and the idea is that the Universe is gradually stretching out, so everything will eventually become so far apart that nothing will heat anything up and the Universe will become cold. So, how cold will the Universe be at this point?
The answer is - pretty much the same temperature as it is now! Thing is, the suns and planets account for very little of the Universe's total volume and mass. Most of space is pretty empty, hovering at -270 degrees Celsius (about 3 Kelvin). If we averaged out all of the suns, it would barely make any difference. It would be like taking a handful of matches to Antarctica, lighting them all and working out what the average temperature of Antarctica would now be. While technically we have increased the average heat of Antarctica, it's by such a small amount as to be barely noticeable. Same principle with the Suns and the Universe. In other words, the thermal energy of the Universe already is pretty well distributed.
There are pockets of heat (galaxies) but once they've cooled down, space's temperature won't have changed much. There will still be lone particles, plus empty space has an energy value associated with it, so the temperature will never drop to absolute zero, but it will probably hover around -270 degrees.