Also, note that chapters 88 and 89 are titled "Time pressure", and the exact date and time is specified repeatedly throughout the text. In addition, there’s something funny in chapter 90: Right before Harry has the hypothermia idea, there's a discontinuity:

[The Headmaster] had vanished from where he was standing over the Weasley twins and come into existence beside Harry; George Weasley had discontinously teleported from where he was sitting to be kneeling next to his brother's side, and Fred was now lying straight with his eyes open and wincing as he breathed.

Right after Harry explains the Frigideiro, there’s this:

Fred and George started sobbing.

Which suggests a time loss (likely someone messing with Harry’s memory, the discontinuity sounds a bit like what Mr. Hat did). The sobbs might be because the twins knew what happened during that time, and realized that too long passed for the spell to do anything.

Harry also looks at the Time Turner when he gets it unlocked, and seems to notice or confirm something.

There’s a lot going on here we’re not told.