My very healthy, full term, no issues DS4 suffered from the same thing for 9 months (about 2 years ago). His fevers would be 104-105...even had a seizure because of the rapid onset one time. My Pedi (who I love) and the other docs in the practice were at a loss. I took DS everytime to the pedi....did blood work, gave strep throat tests, checked his ears, urine cultures......all fine. My older children (DDs 7 & 5) did not have anything. The fevers lasted for 4-5 days and were VERY predictible. Alternated Tylenol and Motril EVERY 3 hours faithfully. The fevers disappeared as quickly as they came on but always returned like clockwork. I live in Boston and took my son to Children's Hospital here.
After some research I found a doctor who was studying the same periodic fever symdrome in his own child. After going to a rheumatologist and ruling out "known" periodic fever diseases, the "somewhat experiemental" treatment was to remove my son's tonsils. He has NEVER has a fever since! The doctor said they rule out everything else and then remove the tonsils.....they have had a VERY high cure rate. I was not anxious to operate unnecessarily on the 2 years old, but we were in somewhat dire straits!
Do some research on "PFAPA" Periodic fever, aphthous stomatitis, pharyngitis and adenitis
Best of luck!