Heather,
These old 80 Series units didn't have a "cool-down" cycle at the end of the cycle. These pre-date the current dryers. So, ... You may have a couple of possible issues: You may have a bad High Limit Therm on the blow tube near the heater. Those are cheap to replace. The kit is Part # 3387134 and includes a Thermal fuse, High Limit Thermostat and a Cycle Thermostat (probably the real culprit). Replace them all. You can get them on Amazon or a local appliance parts store.
The most expensive item, and the last in the line of heat controls (aside from the heating element which you have already replaced) is your Timer.
I would need to know the Model # (found on the inside of the body hidden by the shut door) to know which Timer you would need... IF you needed to replace that. My suspicion is the Therm set with the bad cycle therm.