Cut out the blown fuse, leaving enough length on the legs to attach an individual terminal block to. (You can extract two brass connectors from the plastic housing of a terminal block - see previous photo).

Connect the ends of the replacement thermal fuse using the terminal blocks to the old legs. Done.

Note: Try to use very small terminal blocks as these will act as a heat shunt, and the whole purpose of a thermal fuse is to blow if it reaches a critical temperature.