It's been said throughout the Wheel of Time books that the trick for not sweating has nothing to do with the One Power. Does this mean that non-channelers can do this?
Short answer: yes, non-channelers can learn, but they may not want to.
In Lord of Chaos, Rand visits the farm and Taim tells him that he teaches Healing
"Even before how not to sweat to death in this weather."
Rand later asks, seeing Sora Grady (Grady's wife) sweating
"Don't you teach the women that trick of concentrating?" Rand asked. "It's cruel to make them sweat when their men don't."
"Most want no part of it," Taim said curtly. "Their husbands and sweethearts try to teach them, but most refuse even to listen. It might have to do with saidin, you see."
The trick relies on a simple concentration/meditation technique and doesn't involve channelling at all:
The method of ignoring heat or cold turned out to be a trick of mental concentration simple enough once you knew how, or so Natasia pronounced.
“The mind must be as still as an unruffled pond throughout,” she said pedantically, just as she lectured in the classroom. They were in her rooms, where almost every flat surface was covered with figurines and small carvings and painted miniatures. These lessons always took place in the teacher’s rooms. “Focusing on a point behind your navel, in the center of your body, you begin to breathe at an unvarying pace, but not as normally. Each inhalation must take exactly the same length of time, and each exhalation, and between, for that same space, you do not breathe. In time, that will come quite naturally. Breathing so, focused so, soon your mind becomes detached from the outer world, no longer acknowledging heat or cold. You might walk naked in a blizzard or across a desert without shivering or sweating.” Taking a sip of tea, Natasia laughed, her dark tilted eyes twinkling. “Frostbite and sunburn would still present difficulties, after a time. Only the mind is truly distanced, the body much less so.”
-- New Spring (prequel novel)