Can adrenal fatigue cause low grade fever? Are progesterone and estrogen levels related to adrenalin and cortisol?

Dubious diagnosis. "adrenal fatigue" is a pop diagnosis, not an evidence-based one. Since true addison[s isn't a febrile illness, this isn't either. I've wondered if the "subclinical addison's" claims might have something to them, but would urge you not to self-diagnose. The danger of self-diagnosis / treatment is missing another real emotional, situational or physical problem. Your doctor should work your temp up.
Yes. The answer to your question is yes. Adrenal hormones are intimately involved in estrogen & Progesterone balance. Progesterone can affect basal body temperature. Hormones in general affect body temperature. Seeing a doctor to rule out infection is important with persistent low grade fever.