I have to replace a blown thermal fuse in my Whirlpool electric dryer (Model LER7646EQ1). Many tips that I have read say to replace the thermostat when replacing the thermal fuse. Which thermostat should I replace? I see there is a cycling thermostat (part # AP3131939) and a thermal cutoff that includes a high limit thermostat (part # AP3094244).

A typical limit kit looks like this:

None of the above limits is the cycling thermostat. It however mounts right next to that fuse here:
I do not know if you can see it all that well but the cycle thermostat sits right there on the blower housing. It judges the temp of the drum. I gotta tell you though,most of time those cycle thermostats stay ok. That would be the LAST thing to replace. None of these parts will beworking right until you clean the lint out of the dryer, the dryer filter housing, and the vent area going to the outside.You need a meter to check each thermostat to see if they have continuity. I will tell you this. The limit on top of the heater element is probably the bad one. If it runs but no heat yep that's it and it's little cousin down below is bad too. Why? Because it is supposed to shut down at 250°F, it allowed the 300°F limit up top to blow. So you gotta replace em both and that's why you gets em both in the kit.

I will go to google images and type in stuff like whirlpool dryer duct
Or kenmore fuse locater. If I see one I like I will save the pic to my pc.
upload it to the site for a better explanation than can be written. I am able to do it from memory, I know what to ask about, because I was in the service business for 25 years and after that I worked for an appliance parts outlet for 10 more years before retiring. All of this is off the top of my head.

Take the screws off and remove the rear cover. Note: not all of them can be accessed from the rear. The princess series has a bottom access panel as does the DOT dryer(dryer of tomorrow piece of crap):D