As far as Everest goes I think the problem is lack of oxygen, not cold.

The temperature conditions simply aren't so bad you can't come up with gear to do with it: the explorations of the Antarctic had to deal with such things a century ago. A badly-equipped climber could certainly be at risk from the temperature but the real problem is oxygen.

"Raising his body temperature" probably means shivering: I'm not sure how much heat the body can generate on demand other than by muscle activity.