I have a friend whose 15 month old daughter has this same problem. They have said it's a 'fever virus' that she cannot get out of her system for whatever reason. She's had 3-4 episodes of it, and it started when she was around 7 months. She's had bloodwork to look for all sorts of conditions but this is the only diagnosis they can come up with. She now keeps a journal where she writes down temperatures, and also how her daughter is acting (lethargic or normal, because sometimes the fever will be around 103 and she'll be playing like she feels fine).
I am a worrywart when it comes to fevers...because if a fever gets too high, you can have a seizure. And once you have a febrile seizure, you are more susceptible to them the next time you have a fever (at least this is what I've been told).
I would insist on bloodwork...not sure exactly what...but with my friend's daughter, they did the CBC, they checked her red and white cell counts...they were trying to rule out more serious medical issues...
There's an infection looming in there somewhere...because that's why we get fevers...to fight off infections. Try to keep a log to see if there's a pattern. Also keep in mind that fevers do tend to spike at night (there's a reason for this but I can't think of it at the moment).
I wish you luck and I hope your little one feels better soon...it's so scary being a mom sometimes!