So, I did the same experiment today... and got the same temp when I woke up 3.5 hours later. I think I will just temp when I wake the first time if it's between 5 and 7 and not worry about it
Update... so just for funnsies I took my temp again... hey, it's my day off, I'm still in my jammies and felt the need to be silly!

So, this morning at 6am it was 98, at 9:30 it was 98 and just now at 3 after a day of moving around it was 98.1... so, when I can't do the same time due to life stuff that we can't control I'm not going to worry about it