Disconnect the Kenmore's power cord from the wall outlet.
Pull the dryer far enough from the wall to reach the hose hooked up to the back of the appliance. Loosen the screw in the circular clamp holding the hose to the Kenmore, using a screwdriver, and pull off the hose.
Remove the bolts in the access cover plate around the edges, using the nut driver.
Remove the back cover and locate the heating unit on the left side. The unit is a stainless steel canister with two oval-shaped components attached to the left edge.
Slide off the two wires on the top component on the left edge. This part is the thermal limiter.
Remove the two screws holding the thermal limiter to the side of the heating unit. Pull off the thermal limiter.
Align the new thermal limiter with the two screw holes on the heating unit and attach it with screws.
Connect the two wires to the terminals on the thermal limiter in the same way the old part was connected.
Bolt the back cover onto the Kenmore cabinet using the nut driver and hardware from Step 3.
Attach the hose to the vent outlet on the bottom of the Kenmore and tighten the screw in the clamp.
Reconnect the power cord to the socket.