This is a physical impossibility to survive without exterior energy sources or significant water.
The temperature of the air is given at about 72 degrees minus 25 degrees Celcius. That is 48 degrees C or 118 degrees F. When the air temperature is above 100 degrees F, the body cannot cool itself by conduction. It has to cool itself by radiation or evaporation of water.
With the ground temperature much higher than the air temperature, cooling by radiation is essentially nil. It is far more likely heat would be *gained* by reflective radiation from the ground, not to mention solar energy.
That leaves evaporation, which is the major mechanism for human bodies to cool. It requires the evaporation of water. The evaporated water carries the heat away into the atmosphere. If the water is condensed, the heat of evaporation is returned to where it is condensed.
Thus, a "stillsuit" receives the heat the body has dumped, and has to release that heat to the environment, without giving it back to the body.
I suspect clever engineering with a compact, high energy source, could do it, perhaps by radiating the heat from a very hot radiator, shielded from the body. But, it requires a lot of energy to do it.
You cannot do it with muscle energy from the same body you are trying to cool.
It is just another suspension of disbelief, piled on many others in the novel. Good science fiction has one, around which the story is built.
I suppose it was a good fantasy novel, with quite a bit of magic disguised as technology.
Could not the energy of heat be recycled as well?
Thermoelectric devices are common. I use one at work every day, both thermocouples and a thermoelectric heat/cool device in our products we sell to government, civilian and military use all over the world.
One device gets very hot when DC voltage is applied in one direction, and gets freezing cold when applied in the other direction.