What can be reasons for my period to delay 8 days so far...could it be the changes in temperature??

Brown = old blood: Irregular periods are one of the most common problems obgyns treat. If this is one time problem it usually resolves on its own. If this is a recurring problem you should be evaluated. Infections & hormonal changes can cause spotting. If there is a concern for pregnancy then do a home pregnancy test . There are many options available to help regulate the menstrual cycle. Schedule a visit.

Not temperature: The temperature won't effect your cycles. If there is a possibility you could be pregnant, you should check a test. If not, there must have been a delay in ovulation. Many things can effect your cycle, including stress.