Looking on the internet, the specific heat of the body is about 3470 Joules/ kg*C and the body raises temperature by approximately 1 degree Celsius as you raise your core temperature through exercise to the point where you are sweating. There are also 4184 joules per dietary calorie. And there are 2.2 pounds per kilogram. So the amount of dietary calories you burn by raising your body temperature to the point where you sweat is:
3470 (Joules / kg*C) * (1 calorie/4184 Joules)(1 kg / 2.2 pounds)*(1 degree Celsius delta temperature) =
So a 200 pound man burns .37*200 or 74 calories going from resting temperature to a sweat at the minimum. Really it will be higher because some of the heat generated is radiated away from the body and doesn't go towards raising the temperature of the body. Also there is an efficiency to burning calories and doing work in the physics sense, this 74 calories is just the waste heat, you will be using some calories to propel your body if your running or moving a weight if your lifting weights. Also there may be a caloric cost for the body to initiate the sweating process, I'm not sure if it's significant though.
So I believe this is why interval training works so well for losing weight, because if this 200 pound person over a period exercised to the point of sweating then let himself cool back down to normal and then repeated 10 times that would be at a minimum 740 calories. This could probably be done over an hour where you jog or run fast enough to break a sweat 10 times alternating with cooling down. Compare this to continually jogging for an hour only burns 640 calories for a 200 pound man.
I think an analogy might be to think of boiling water, it takes a very high heat to get water to a boil, but once it's boiling the heat can be turned down to maintain a boil. It may be that the body expends a lot less energy to maintain a sweat and keep the body temperature up than it does to get to that temperature in the first place. So to use the most energy you would heat the water to a boil, then cool it off, then repeat. And it seems to actually be the same for exercising that getting to a sweat through exercise then allowing your body to cool and repeating actually seemingly paradoxically uses more energy than solidly exercising over the same interval. And of course it takes a lot less effort because you are resting a good percentage of the time.