I’ve been a sick monster recently and it got me contemplating the mysteries of fevers.
I can answer the first. Your body temperature fluctuates throughout the day. Your lowest temperature is in the early morning, and the highest is in the late afternoon early evening.
The second I can offer an educated guess. You tend to feel cold when your body is trying to increase temperature. You tend to feel warm when your body is trying to decrease it. So perhaps your body is trying to find the perfect temperature to balance killing off the virus/bacteria and keeping your other metabolic processes at proper levels.
Just to add to what BigT said, there is a diurnal variation to body temperature which persists even when someone has a fever. In other words, there is a natural cycling of body temperature with the highest temperature occurring late in the afternoon and persisting to early AM. Body temperature starts to drop later in the morning, say around 04:00 (give or take). The drop corresponds to a rise in the level of blood cortisol, a hormone with many properties including lowering of body temperature. Levels of cortisol peak around 08:00.
In terms of fever causing you to feel hot/cold, there is a natural sequence governing fever. Specifically, as your temperature rises, you feel cold and may even start to shake or have rigors (this is a manifestation of your body generating heat, just as would happen if you were stuck outside on a freezing day - you’d start to shake).
When the body (and specifically the hypothalamus) no longer wants to keep the body temperature so high, signals are sent to dissipate heat. Again, just as would happen if you were sweltering on a hot day, you begin to sweat and get flushed (both of which cause heat to be lost from the body).
To a large extent, then, if someone is having shaking chills (rigors), or is having drenching sweats (especially at night), it’s usually tantamount to them declaring that they are having fevers. This is often seen in patients with certain cancers or chronic infections even if they aren’t aware of, or don’t think they’re having a fever.
Hope you don’t mind me adding another question here. One thing I’ve wondered for a while, but been too lazy to ask.
Why do you become weak physically, with a fever? I’ve had everything from not being able to lift as much as usual, to being effectively paralysed from the waist down when I’ve been running a high temp.
Although fever itself does seem to make you feel awful, and weak, I suspect that the reason weakness is often so prominent a symptom is because what’s causing the fever is also causing the weakness. Specifically, fever is often due to high levels of blood interferon and interleukins (i.e. cytokines). These substances are released into the blood when you have a virus infection, cancer, etc. They not only can cause fever but also can cause a whole host of other, non-specific effects including feeling like you’ve got the flu (weak, achy, . . . ).