will this part cause the dryer to heat throught the cool down cycle
Answer Kevin, The temperature switch would not be the problem, usually. Your first check should be at the heater element 279838 and wiring.
If the wires or the element have separated and have shorted to chassis ground that could leave the heater element energized, and cause the dryer to heat through out the complete cycle. The next check would be the timer heater circuit contacts. When the timer advances into the cool down cycle, the contacts should open the last 5 to 8 minutes eliminating power to the element and allows the drum and clothes to cool.