Body temperature fluctuations while sleeping

Does the human body temperature normally fluctuate at night when you’re sleeping?

I ask because on several occasions I’ve woken up in the middle of the night (normally 2-3 hours after I’ve gone to sleep) feeling really crappy and feverish - body aches, slightly nauseous. Then, when I take my temperature, it’s around 96.5. If I get out from under the covers, I get very chilled and have uncontrollable shivvering. I pile on the covers and maybe put on some fleece underwear to try to warm up. Eventually, I will warm up, my body temp gets back to around 98.6, and I have to start shedding layers of clothing. If I manage to get back to sleep, I’ll be very sweaty when I wake up normally.

Do I need to replace my thermostat?

From what I’ve gathered, a two-degree-Fahrenheit change in your body temperature is not at all abnormal. From this page:

I guess that begs the question: do I normally drop down to that temperature, and I just happened to notice it because I woke up?