What kills you first in space?
Space is something like -450F. That won't take minutes.
Space is a near total vacuum. Temperature doesn't quite translate to what it does in an atmosphere.
It also depends on if you're shadowed by a planet e.g. the Earth, and how far away from the Sun you are. If you're not then its going to be the opposite - extremely hot. Check out the difference in the temp on surface of the moon between night and day.
You also need to consider kinematics of heat transfer.
For example, when its well below freezing and you're near a body of water, its always better to be on land despite the temperature in the water being warmer - above freezing (otherwise it woudln't be water).
Without a thick fluid to conduct / convect away heat, that leaves only radiation as the form of heat toss. Which is relatively slow. Our bodies are going to keep a reasonable temp for some time - especially because our bodies are heat engines anyway.