how long does it take for the human body to radiate its heat away to freezing in space?

You could calculate it with Stefan-Boltzmann law of radiation, if you quess the thermal capacity of human body (http://sol.sci.uop.edu/~jfalward/heattransfer/heat... should hold enough formulas...). But I guess you are interested in surviving hard vacuum (in space). In that respect, the time it would take to radiate heat away is so long that the effect is truly insignificant. The primary threat is of asphyxiation: in the low pressure environment, normal gas exchange of the human body will cause the rapid deoxygenation of the bloodstream (even if you somehow supply oxygen to breath). You can find comprehensive information about it and other threats of space from http://en.wikipedia.org/wiki/Human_adaptation_to_s... .

Also http://en.wikipedia.org/wiki/Vacuum#Effects_on_hum... holds interesting information about this subject.

The interesting thing is that a human body would boil, not freeze in space. The reason for this is the lack of pressure, which lowers the boiling point of water to almost absolute zero.

Assuming that you are naked, you will freeze very fast. The more protective your suit, the longer it will take.

I'm gonna guess, 30 secs, one or two Min's. the longest id say, 20 Min's?

Eating doughnuts helps.