...Not immediately, that is. There is a bunch scientific reasoning and experiment to back this up. The upshot is that since space has 'nothing' in it, if you end up there, you are in the 'radiative regime' when it comes to freezing. The heat that you have doesn't convect or conduct away from you very easily at all. You radiate your heat away much like a blackbody. This takes days, weeks, or months, I imagine.