No, it usually go down, but it can fluctuate a bit while you're on your period. In general, temps will be lower in the first half of your cycle, then rise the day after ovulation and remain high until you get your next period. Hope that helps :-)
Does body temperature go up before menstruation? If yes, how many days usually? Thanks
It certainly is possible to be pregnant and still have a period, I have heard of many women that this happens too. However, it is also not unusual for your temp to stay elevated or eratic during AF because of residual progesterone. If in doubt I would take an HPT. Good luck : )