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Your info suplied is either incorrect or faulty. The tibetan monks would have to keep their body temperatures high, like you said, sweat cools the body and the wet cloth is already their however since the body is going to have to keep high temperatures to dry the cloth off completely and the body would therefor have to constantly supply sweat because you're insides would still be heated, even if there is a wet cloth wrapped around you. As far as your body would be concerned you will still be hot and it would need to cool you therefore supplying more sweat.
If this is faulty then read this. You'd have to keep hot through the whole of the excercise if you are to completely dry of the wet cloth. The wetness would gradually decrease and you'd be hot and the body would therefore have to start supplying sweat. Even with this the guy never actually reports being hot all he says on how he felt is
Hmm...how to explain...
Okay, to understand this, you need to know a little bit about how the body senses information. Precision readings are very rare. The body is not very good at figuring out what level things are at. For instance, the body cannot sense speed. It cannot evaluate how fast you are moving without outside reference. What it can detect, however, is acceleration or deceleration. In other words, what the body can detect is
rate of change.
The same thing applies to heat. A person with a fever, unless he is stuck in bed and has little else to think about, can rarely detect a fever. They usually detect the other symptoms of a cold before they check for fever. Small children, whose hyper little bodies are always eager to overreact, can produce a full fever in a little under ten minutes, and thus produce a sizeable enough change to be detected. Otherwise, the only place most people can actually sense excess heat is through the ears, where the membrane is thin enough for dissipation (rate of change) to occur.
So let's get back to our intrepid and waterlogged monks. Their bodies, unofficially, have three levels (warning: this is not biologically correct; this is greatly simplified) of heat dispersal. Level one is the standard radiation from the skin. Level two involves increasing circulation to the skin so that the rate of radiation increases, due to the higher quantity of warm blood at the surface of the skin (this usually produces a very 'flushed' appearance). Level three requires the addition of evaporation (sweat) in addition to radiation.
When our young monk initiate sits in his cave and is draped with the wet blanket (in more civilized societies, we would probably call this hazing, but what the heck), his body, through the power of intense meditation, begins producing heat. In and of itself, this is nothing unusual to it. The first line of defense against infection is usually an increase in heat, such as a fever, to kill bacteria. The thing is, though, that the body really can't tell how hot it is making things. The body has a very limited amount of information to work with. It will stop making heat only when certain conditions have been met; either the bacteria must be gone, the mind must be in danger (considering the speed at which this can happen, this is the least preffered trigger), or if the cycle is broken externally (through the use of ice packs on the body).
Now, the monk's body is not aware of any infection. And it is told to override the ice pack clause. It simply understands that it has been ordered to produce heat and that is that. In order to keep the organs safe, it shifts to level two of heat dispersal. There is a certain amount of hot blood going out to the skin, and there is a certain amount of cold blood coming back into the core body. Satisfied that heat exchange is taking place, it then checks to make sure the mind is within tolerance limits. The mind is fine. It checks the body again and finds it is still too hot, so the process continues. As long as there is a decent rate of heat exchange and the mind is safe, the body is not too concerned with time. The body does not need to switch to level three, because the rate of change is satisfactory. Only if the heat within the body increased to a level at which there was danger to the organs would the body react and increase the rate of heat dispersal. If it doesn't need to, it won't (the body is lazy like that).
Now, this can be done with a single sheet, although the monks actually do it the entire night and are evaluated on the number of sheets they dry out. There is, of course, a certain fluctuation of temperature as dry sheets are removed and wet ones are replaced, however the body, only interested in the rate of change and the safety of the organs, won't react dramatically. Since it only senses rate of change, and not actual temperature, there is a certain level of heat retention which acts as a buffer zone.
Did I explain that well enough?