If the dryer runs and gets too hot the fuse will melt.But the dryer will still run. So if the fuse is good(continuity) and the dryer control(cycle) thermostat is also good then you should have power going to the gas valve assembly when the machine is running unless the timer is in the no heat or wrinkle free/cool down mode. When the gas valve assembly is energized the flame sensor

mounted outside the burner chamber detects the heat from the ignitor. When the heat is very intense then the sensor shuts down the ignitor



and that frees up the power so that the coils can be fully energised and open the gas gates. The gas comes out and hits the red hot igniter and you have ignition. It stays on for maybe 2 or 3 minutes or until the control thermostat is satisfied and shuts down power to the gas valve assembly. So...
If your gas dryer has a good flame sensor and a good igniter AND the dryer will work some and quit, replace these:



The coils get hot and quit on these machines when they get a little age on them. It is aggrevating because it is a hard to diagnose thing. But well worth the 20 bucks.