Perhaps the cap is a separate part to be pulled off the old thermostat and pushed onto the new one.

That is the first thing I tried, but I couldn't pull it off even with pliers. And on-line the images of the replacement piece show it with the cap.

I went back to the appliance parts store and they told me about 4 years ago the part changed and doesn't include that little plastic cap anymore; I have no idea if that's true or not. Anyhoo, I went ahead and installed it and put the dryer back together. The dryer is now working/heating.

I'm just a very not-very-handy stay home Mom and didn't want to pay over $100 to have a repair person come do this. I figured dryers were pretty simple, and could at least learn how to repair it. When I saw that the new piece looked different I got worried.

Glad you figured it out. So many people are afraid to do repairs or maintenance and think they need an expensive "professional" for every little thing. Today I was installing some dimmers and couldn't get them to work. After a while I thought, why don't I just try reversing the wires? Voila!