I determined that the heater assembly was the issue. I purchased a multimeter with an auto-read function. I then pulled the heater assembly parts out through the vent gate and tested the thermostat, thermal fuse, and heat coils for conductivity. The thermal fuse was the only part that did not set off the meter.
I ordered the thermal fuse from AppliancePartsPros.com, however I quickly realized I only ordered the fuse and not the entire fuse assembly. I contacted AppliancePartsPros.com through chat and they quickly fixed the issue.
The part arrived in two days, I screwed the new thermal fuse in, reattached the wires, and had clothes drying in a matter of minutes.