The thermal fuse located on the side of the thermal unit housing recently popped. I've replaced the fuse and no wires are burnt and everything checks out continuity wise. We're now getting a burning odor when the dryer is running.
I'm thinking of getting a new heating element to be safe but not sure if that's the cause though

These driers will do that when the lint builds up like concrete on the inside of the air ducts. The heating elements have zero to do with anything. It's so full of dirt the next thing it will do is to catch on fire and burn down your house. Also, the sensors get blocked from sensing when the dryer is dirty. You have to totally tear it down piece by piece. Halfway cleaning it will not work because all it takes is one clogged up air passage or dirty sensor. You need to totally tear it down and scrape out and wash all of the parts except the motor, which you vacuum out. You can go to YouTube to see videos on how to take it apart, but do a very good job or it will fail again quickly. I would get a new belt and change it while you have it apart and get some white lithium grease and grease any bearings you find. You need to clean out a drier every two years, at least, according to the manual. You just unplug the wires from the sensors and remove ductwork that they are attached on and clean the entire thing with soap and water. Make sure you go all through the dryer and get all parts like the blower fan and housing (it has to be scrubbed and washed out), vacuum out motor well and clean exhaust. Mark all wires you unplug so you know where they go. If you leave any dirt in the ducts it will blow another fuse quickly or will not maintain the temperature correctly. This is an easier job than you would think. Make sure to clean around all of the sensors, if it has them. You can check them with a meter and the chart in one of the manuals, too. See: Dryer vent cleaning prevents fires - YouTube and: Cleaning out a dryer with top lint cleanout - YouTube
Cleaning out a dryer: By a woman 2 of 2 - YouTube
https://dl.dropboxusercontent.com/u/...g%20Dryers.zip