I don't have these symptoms, but I would have to wonder if the alternating of your predisone doses is to blame....
If you are on high doses of steriod for prolonged periods your adrenals get used to this... abruptly lowering can cause many of the symptoms you describe, I believe including the elevated temp.. I wonder if your adrenals are sensitive to this high, then low, then high dose... they are a bit confused? Just the first thought that comes to my mind...