What would cause a clothes dryers thermal cutoff to keep tripping?
How did you check the vent?  Mine had an open airway, but after years of use, I picked up a cleaning brush and was amazed as how much lint came out of the vent.  If your dryer is anywhere other than on an outside wall, I'd pickup a cleaning kit just because they are nice to have and reduce your fire risk. Here's one from Amazon:



That reminds me, I should clean it again soon.