Move the dryer away from the wall, and unplug the power cord from the wall outlet.
Loosen the screw on the vent clamp securing the vent to the rear of the dryer. Inspect the interior of the vent and clean it using a shop vac if it is clogged. Often, a clogged vent is the reason that the high limit thermostat tripped.
Remove the rear panel from the dryer by unscrewing the screws around its perimeter.
Locate the high limit thermostat, which is secured to the side of the heating element. The heating element is on the bottom of the duct on the right side of the rear of the dryer, and it has two terminals its left side.
Pull the wire off the top terminal on the high limit thermostat.
Pull the thermostat off the dryer terminal and discard it.
Insert the hook on the high limit thermostat opening into the hole on the top of the new thermostat, and then connect the new high limit thermostat to the heating element terminal.
Connect the wire connector to the terminal on top of the high limit thermostat.
Reassemble the dryer by reversing the steps taken to take it apart.
Restore the dryer's power supply and then move the dryer back against the wall.