You should decide at the beginning of BBT temperature charting what you consider the beginning of a new day, either after midnight or when you wake up. Both choices are OK.

There is sometimes a question when you should consider the beginning of a new day. Do you go by the calendar and does the new day begin after midnight? If you make love at  1 minute after midnight, is that a new day or the previous day? Or does a new day begin in the morning, when you wake up?

For purposes of BBT charting it does not matter what you consider to be a new "day". The best thing to do is that you should decide at the beginning of the cycle what you consider to be the beginning of your new day. And then you should be consistent with charting it for that cycle. If you decide the day starts after midnight, then that's OK, and if you decide it starts when you wake up that's OK too.

Either way, be consistent.