Look carefully at the temp above on that chart.  From midnight it plummets to it’s lowest in the whole of a 24 hour period.  It stays that way for some time and then towards waking at 7-8am it starts to climb.  I am wondering if the rapid decline of the body temp somehow triggers something where the HPA is concerned when it get’s TOO low.  I.e. at it’s lowest point just before cortisol is produced on the same charts.  You will see the blood pressure follows the cortisol curve exactly, but that the body temp is doing something completely different for a while.  

All I know is that for temp to start climbing back up, you would probably need cortisol and blood pressure to be doing something, and that cortisol rasing would precede the ability for the blood pressure to raise.  Thats why I think it is the body temp reaching a certain low levels that prompts production of ACTH and thus cortisol.