Outer space is in reference of the void between units like solar systems, where extreme proportions start to grow until impossible numbers. This question was proposed several times with different answers, but always less than 7ºK. It seems that there's a background radiation that is capable of warming the entire and incredibly vast outer space.
Near our star, the temperature might reach more than 2.5 megakelvins, more than enough to vaporize matter. A rock substrate doesn't stand 10.000K, so the rest is extra energy although fortunately none should try the experiment!
Another source of temperature are interestellar clouds (7000K) and some nebula (~10000K) but not all. It's believed that in intergallactic space the temperature could be near 10 megakelvings, making any trip worse than crossing the desert with a bike. At this temperature, the electrons may get very excited.
Finally, after being pulled by cosmic filaments —if they exist— the gas could gain more temperature, maybe 100 megakelvings. Another captivating number is the maximum possible temperature of matter, the so-called Plank temperature and without doubts applied primarily to Big Bang, in the order of 1032!