1. Why is there an increase in my body temperature during exercise?

Our bodies are always producing energy through chemical processes which of course produce a little bit of heat.  When you exercise, this process cranks up according to how intense the exercise is and how many muscles are involved.  So, lets say you are just walking with your friend.  There are a number of muscles that take part but you’re not working very hard.  Thus, your body temperature doesn’t change much.  Now say you are training for a boxing tournament.  Now you are using a lot of muscles AND you are working your brains out.  So, although your body temperature during exercise would only be a little higher than walking, you’d produce a ton more heat.  More on why that is in the next question.

2. What should be my average body temperature be when I exercise (if it’s a range or depends on gender/age/other factors, etc.)?

The amount one’s temperature increases is solely a result of the intensity of the exercise and the muscles involved.  For instance, one can be intense doing pullups but will not produce as much heat as sprinting for the same amount of time.  More intensity and muscle involvement = more heat.
However, the reason your body tends to maintain an average temperature of 98.6F is because it works best in this range.  Not surprisingly, it “tries” really hard to maintain this temperature.  So, during exercise, you give off lots of heat.  It’s mainly from sweating which is your body’s way of cooling down.  When sweat reaches your skin, it mostly evaporates into the air, along with the heat it holds.  It turns out that this is pretty effective and as a result, you are likely to see an increase of no more than 3-4 degrees in average body temperature during exercise (assuming your are drinking adequate water.)  If you aren’t drinking enough, you can’t disperse heat fast enough and the increase in body temperature results in heat stroke, then coma, then death.

3. How long does body temperature stay elevated after exercise? Why does it stay elevated?

After exercise, your temperature is likely to remain elevated for a little while.  This is for two reasons.  First, your body is “catching up” in energy production.  In other words, it keeps producing energy to replace what you used exercising.  Second, it disperses the remainder of the excess heat it produced.  I did say sweating worked pretty well but its not perfect, so it takes a little time even after exercise to rid your body of all the excess heat. Even for the most intense exercising, this will probably not last more than 40 minutes or so.  More like 20 for your “standard” exercise.