Hopefully the repair will go smoother than your diagnosis
Remove the screw holding the large disc first, then remove the long screw holding down the heater bracket on the right. Lift the heater up and out of the housing. The thermal fuse is mounted on a small tab tucked into the side of the heater housing and lifts out. The eaiest way to install the new fuse is to position it in the little bracket, then attach the 2 white wires so you can guide it more easily into the slot. There's not much room for fingers there as it is, so the wires will help you hold it while you place the heater and long screw back in. Be sure the long screw also goes into the tab on the fuse plate when you tighten it down. Also, be sure and replace the large disc before you put it back together.
Don't forget the vent thing...if you don't have the right exhaust on it, the fuse will blow again soon. Maytag dryers must not have thin foil duct. As of yet, we still do not know what gave off the burning odor your wife mentioned.