Since it is so constant, it sounds like there might be a physical cause. Talk to your doctor, and ask if he or she will check your hormone levels. (You can get hot flashes and cold flashes in response to changes in your hormones.)
If the doctor runs tests (also maybe thyroid) and hormonal reasons are ruled out, and you think it is perhaps rooted in anxiety, try anti-anxiety techniques. Some are:
- Focusing on breathing: Breathe slowly in and out while counting to five each time
- Focusing on the senses: Touch something soft, or eat something
- Applying grounding techniques: Breathe slowly and focus on your surroundings, including sounds, smells, and tastes
But before you decide it's all in your head, do get your body checked. A flawed internal thermometer can be caused by something physical.