It sounds like menopause, but it's important to have your thyroid checked periodically as it can go bad at the same time.
Fibromyalgia does cause body temperature changes like you are describing. It also could be Hypothyroidism. Get your thyroid checked. With me, I sweat like a horse even when it's in the 40's and I'm not wearing a coat. I have fibromyalgia but have also found out I have a thyroid gland that goes to hypo to normal back to being hypo about every three months. good luck and I so feel your pain.
Please look into possible underlying adrenal and/or thyroid dysfunction.
Dr. Barnes Basal Temperature Test will indicate any relevant thyroid or adrenal imbalance, barring any presence of infectious conditions.
Please do an online search for this test and follow the simple instructions
Adrenal fatigue and hypothyroidism can be both present and the adrenal fatigue may be a cause for hypothyroidism or at least a co-factor.
In such a case the adrenals must be addressed first before thyroid dysfunction (secondary) can be treated properly.
Unfortunately conventional endocrinology does fully not recognize the above, leaving a large number of suffering patients in limbo, underdiagnosed, misdiagnosed and consequently "mistreated"! Lol!
Hypothyroid is consistent with temperature tolerance within a narrow range, basal temperature below 98.60 and with usually no orthostatic hypotension among a myriad of other symptoms.
Adrenal fatigue is consistent with often extreme fluctuating temp. regulation, basal temperature of 97.80 and lower with frequent occurrence of orthostatic hypotension, salt and/or sweet cravings among many other symptoms.
Need more details, let me know.
Wishing you all well.
Love, Light & Abundance.