I have a little space heater with a burned out thermal fuse.

All the web hits for thermal fuses seem to be about big things like
clothes dryers.

At home I had a card with a selection of thermal fuses, but I never
knew what value I should use. The original one didnt' have a value
listed iirc. Or maybe getting hot made the number unreadable.

In addition, I was afraid to solder the thing in. The originals are
always riveted. I can't rivet. Can I solder?

Finally, I won't be able to buy replacement fuses at hardware stores,
will I? Just at a few online suppliers, unless I happen to be in the
same city where one of them is located?