One of my relatives (old) had this kind of mysterious fever. It used to go away in 3 days, and then used to come back within around 5 days. The first day, fever was high (like 103), then it used to reduce over the next 2 days. The fever was high promenantly at night.
'Modern' medicine and 'specialists' got stuck with lung infection and various tests which gave no results. The blood test results were erratic and inconsistent pointing to a mix of all diseases. This had been going on with 6 months.
Then he though of taking a remedy of alternative medicine based on Indian origin (something related to Yoga). The practitioner said this's a result of food allergy. Apart from giving medications, he a black and whitelist of foods to avoid and prefer.
And that was it ... fever was gone.