No, it's not a very fast process. Dehydration through respiration is insignificant compared to dehydration through perspiration; and in any case, dehydration is still a much slower death than heat stroke. It's only possible to die from dehydration in a high-heat low-humidity environment because the heat index is low enough that heat stroke is less likely, because the body is still able to cool itself through perspiration. Even in very hot/dry climates, dehydration typically takes days. Most often, heat stroke will kill due to lack of perspiration reducing the body's ability to cool itself.