Additional Study Information: We are conducting a research study to see if hormone therapy (HT) helps reduce hot flashes and night sweats in women living with HIV in the late menopausal transition (similar to what is known as perimenopause) or early post-menopause (the time after the final menstrual period or after removal of both ovaries). If you were assigned female sex at birth, are 40-60 years old, are in the late menopausal transition or early post-menopause, currently having moderate to severe hot flashes and night sweats at least every week, and you are living with HIV, you may qualify to participate in this research study. This is a 2-part study. Part 1, which has no study drug, will last up to 5 weeks. At the end of Part 1, if you meet criteria and choose to participate, you will enter Part 2 of the study which will last about 12 weeks. Part 2 participants will be randomly assigned to one of 2 groups. One group will receive Hormone Therapy consisting of a transdermal estradiol gel (to be rubbed on skin) and a progesterone pill to take orally, and the other group will receive placebo (a product that has no active ingredients). If you decide to participate, you will receive a minimum of approximately $175 in Part 1 and, if eligible, $275 in Part 2.