No offense, but I don't think you're trying hard enough.
Basic science 101, how does heat transmit? I'll give you the three
only ways: Conduction, convection, and radiation. Now, considering space is an empty void, there's obviously not much to conduct or convect heat to. So our only option is radiation. Unfortunately, we are not stellar objects. The amount of heat we emit via radiation is extremely low. I'd love to see you prove me wrong on that.
And on the oxygen effect, that is true. But there is no explosion, freezing to death, or any other gruesome instantaneous death. Your main poison in outer space is suffocation. And that's easily solved by keeping the oxygen recycling contained to the head section of the suit. A breech to the head equals a dead man anyhow.
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