Sounds more like possible infection -- the dose of 75mcg Synthroid is low for a total thyroid -- check TSH, Free T4 and Free T3 to see current thyroid status. But hypothyroid is not likely to be cause of "fever".
The initial high white count suggests infection, the current low-grade temp and subjective fevers are less specific. Would keep working with the internal medicine doc to get to the bottom of it.