More specifically, in chapter 56:

Kill her and then bring her back, came the next suggestion. Use Frigideiro to cool Bellatrix down to the point where her brain activity stops, then warm her up afterward using Thermos, just like people who fall into very cold water can be successfully revived half-an-hour later without noticeable brain damage. Harry considered this. Bellatrix might not survive in her debilitated state. And it might not stop Death from seeing her. And he'd have trouble carrying a cold unconscious Bellatrix very far. And Harry couldn't remember the research on which exact body temperature was supposed to be nonfatal but temporarily-brain-halting.

He forgot to get his time-turner unlocked, but he remembered to look this up, evidently.