InspectorD, that same switch that's supposed to protect from overheating failed on a dryer I had, shut off the heat and left me with a dryer that would spin, blow a lot of cold air and seemingly never dry my clothes.
The most common 2 problems have been covered, one hot wire not hot at all, clogged vent.. The thermal cutoff switch and the heating element are the next to check on my list. Then the main control switch, the temp control switch.. You need a meter, or a repair guy to look and see what's wrong if you have good power and no clogs. The thermal switches are mounted directly on the heating element housing. If you do the repair yourself, take the time to clean the air ducts and the louvers, your dryer will appreciate it.