I find that on long desert treks, I experience noticeable heat adaptation (less sweating) after 5 to 7 days.
There are a couple parts to heat adaptation in a dry climate and less sweating isn’t one of them. Heat adaptation in a dry climate means your body sweats more and sooner in response to an increase in core temperature.
There are multiple sources, but from this one (https://www.sciencedirect.com/science/article/pii/B9780444640741000318):
A critical physiologic change that occurs during heat acclimation is the “training” of sweat glands to produce a greater amount of sweat. This leads to a progressive increase in whole-body sweat rate for a given work intensity or core temperature
If someone says they sweat less after 5-7 days in the desert and they consider this as being “heat adapted”, then I think they are sweating less because they have become progressively dehydrated during the trip and have total lower water volume. From the same paper as above:
As water availability in the body decreases, so does the ability to sweat and increase skin blood flow during heat stress (Horstman and Horvath, 1972). Dehydration increases the core temperature at which the onset threshold for skin vasodilation occurs and decreases sweat rate for a given body core temperature



