I wasn't sure exactly which of the two parts was the problem as I had read that both could be the problem. I took apart the dryer following an easy step-by-step video and swapped out the heating element assembly and the thermostat. Putting the dryer back together was pretty simple and when I tested it out, the heat was working and the dryer was running like it should! I'm not the best with tools and repairs but even I could pull this off.
The only issue I had was there was a screw holding the old heating element assembly in that I couldn't reach with even a stubby screwdriver. I had to run out and buy an offset screwdriver and using that was a little annoying but it worked. Otherwise the rest of it was a complete breeze.