When a female is on her period does her body temperature go up or down?

Basal body temps: During the first half of the cycle, the temperature is at a normal baseline. During the second half of the cycle, basal body temperature increases and stays elevated until her period, when it goes back down to baseline.

Body temp goes down: In a woman's cycle her temperature goes up about 1/2 of a degree at the time of ovulation, and goes back down around the start of the period. This is related to her Progesterone level, which rises at ovulation and drops right before the period. To check this on yourself you need to check your temperature first thing in the morning before getting out of bed, called basal body temperature.