Can only getting a couple hours of sleep a night for about a week cause your body temperature to feel as though it's higher than normal? or make you feel nauseous at all?

Yes. It is important to get adequate, usually 8 hours/day, sleep for optimal health. For healthy diet: http://www.choosemyplate.gov/., exercise 30 minutes/day, drink enough water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. Get HPV and Covid vaccines. Wish you good health!

Yes, sleep deprivation can give people flu-like symptoms. Work on waking up consistently and then relaxing activities prior to bedtime to see if this helps. Should take 24-72 hours.