I think I'll solder, with a heat sink far from the end of the wire to
be soldered and nearer the fuse.

One thing I was taught LONG ago with "heat sensitive" components was to use
ALL of the lead length AND put some kind of "heat sink" between the solder
joint and the component. A "hemostat" type clamp works just fine, thank
you.

Do that and your thermal fuse will not even get "warm to the touch" when you
install it.