Her doctor can prescribe antihistamines in larger amounts. The doctor can also use the newer antihistamines, such as cetirizine and loratadine, two antihistamines that do not cause drowsiness. Your wife should not exercise on a hot day. If she can find an air-conditioned club, the air conditioning might stop the rise in body temperature. Have her try it before she signs up for a membership.
Air conditioning is an iffy proposition when it comes to prevention of cholinergic urticaria.
Drinking cold water while exercising helps minimize the rise in body temperature. On the bright side, many with cholinergic urticaria are freed from its grip in a few years. I am a serious bodybuilder. I exercise every day. I vary the exercises so that I am not exercising the same muscles two days in a row.