Dont worry too much if you wake up in the few hours before your due to take your temp, as long as you go back to sleep and dont get up at all.
A small change (if any) in temp that may result is not going to make any difference, remember BBT charting is all about looking at the overal picture of your charts, not every little temperature.
If you really want you can always write a little note on your chart on that day to say that you woke up early then went back to sleep...

For the record, my thermometer beeps to, probably takes a minute I think although im sure some days it seems to take longer than others! that might be just because it is 5:45am and im still half asleap!

DOnt forget to stick it in the same place in your mouth every time... (if you do it orally obviously!) I have been told just under the tounge against that bit that 'holds' your tounge down (im sure it has a name!) is the best because your tounge has heat spots under it.