Use a razor knife and carefully cut away the silicon insulation around the thermal cutout.

Note that the cutout is a 115 degree C 2 amp device. I replaced it with a Panasonic EYP-2BN110 which is available from DataAlchemy on Amazon Marketplace.

Clip the old unit out and melt a blob of solder on the wires that stick out. Then clip short the leads of the new thermal cutout so that they just reach the exposed wires.

Hold the thermal cutout as far away from the device as possible with needle-nose pliers as a heatsink so that the soldering iron doesn't blow the fuse and quickly solder the fuse in place.

Now thread a bit of electrical insulation around the cutout to cover the exposed wires. Do not use more than a layer or the cutout may not operate when it is needed.