It's to do with the hypothalamus. 

What Causes Temperature Sensitivity 

Body temperature is regulated by the hypothalamus. The hypothalamus is a section of the brain responsible for hormone production. It is considered the link between the nervous system and the endocrine system.

The hypothalamus not only controls body temperature. It controls energy levels, the sleep cycle, muscular function, circulation, the gut and defense against infection.

Most fibromyalgia symptoms seem to be due to imbalances in the hypothalamus-pituitary-adrenal axis (HPA axis). These three glands work together to control hormone levels. Disruptions in the HPA axis seem to be at the core of fibromyalgia.

Thyroid hormones also play a role in regulating body temperature. An overactive thyroid (hyperthyroidism) can cause a person to feel too hot, while an underactive thyroid (hypothyroidism) can cause a person to feel too cold.

The thyroid gland is under the control of the pituitary gland. The pituitary gland itself is regulated by the hypothalamus. Anything that disrupts the HPA axis will also suppress thyroid function.

Yup , I sweat even when it’s not hot 🥵 then I’m freezing. My body does not regulate its temperature ever since fibro struck me .

Yes I sweat for the first hour after I'm at work on the back of my neck.

I have the worst temperature sensitivity. I can't handle summer heat, hot tubs, hot showers.... I have to stay in air conditioning as much as possible during the summer. And I can't handle the cold either so I'm the winter I have to stay as warm as possible.

I do too!