Just solder it then heat shrink
Good luck with that! It can be done but to do so so the connection is secure, without blowing the thermal fuse from the heat of the soldering is a royal PITA. Also, mains connections must *NEVER* rely on solder alone, but must always be mechanically secure before the solder is added, so you'd need to form loops in the ends of the thermal fuse leads to hook the mains wire through, which would significantly reduce the lead length available to heatsink it to stop it blowing, and significantly increase the time to fully wet the joint, increasing the odds it blows as you solder it.
It is going to be really challenging to solder a 87oC thermal cut-off but with proper technique I think it could be done reliably. However, heat shrinking it reliably is going to require some witchcraft skills.
Yep, I wouldn't tackle it on a bet, without a custom fitted solid copper heatsink to clamp over the fuse body and leads + plumber's freezing spray to chill it right down before hand!
Yes, I need it, something like that...

Yep, that will do the job. So will Chinese knockoffs of that brand-name ratchet crimper at a fraction of the price. Don't get the non-ratchet flat plate scissors style tool with wire strippers and bold cutters built-in as it very difficult to get enough pressure to make an electrically and mechanically secure crimp, and its far too common nowadays for them to be made of far too thin mild steel that buckles sideways under load.
If you are anyway near a good 'big box' hardware store, see what they've got on their electrical aisle, otherwise trawl thorough this amazon search:
https://www.amazon.com/s?k=ratchet+crimping+tool+terminal+kittill you find one that looks like the above, with a terminal kit including ring terminals. I wouldn't trust a crimp ferrule as they are intended to deform slightly for good contact in a screw terminal so have much thinner walls than a regular crimp terminal, and usually less crimping pressure, so avoid those kits for this job. $25-$30 should see you good, with a tool that will last you for years if you look after it.