Replace a one shot thermal fuse with a resetting one
You could try a "Bimetal Cutout". (It's a bimetal switch, which performs a thermal cut-out.)


Image from cantherm.com

These act like you might expect: They are normally closed, and open when the temperature rises above a certain threshold. They close again after the temperature drops down (including some hysteresis).

You can find them for 250V+, 10A+, and in the 110C range.

Note that you may have a difficult time fitting them in the same tight space.