i'll double down on what james_s said as the purpose of a thermal fuse or switch in a motor is to protect it from burning up. so make sure the thermal switches case will conduct the winding heat like the old one would have so it will open if it gets hot.
As James said, you could bypass the fuse to test the motor, and likely its what id do myself to make sure the motor is otherwise functioning. But please don't run it that way permanently as its disabling a safety feature. That feature is there to keep worse things from happening, like potentially a fire or a meltdown.
considering the fuse already went once, you have to ask yourself why it went in the first place, could there be something causing it to overheat that will happen again. If you happened to have an explainable reason, the fan was jammed, then you are probably in good shape.
I also realized none of us actually answered your initial question, how do you know the thermal fuse needs replacing. its a simple resistance reading across the fuse, if its open, its bad, of its low/0 ohms it's good, and don't do that check with it plugged in. also if you bypass it, like James was talking about, the motor would work. that's also a way to confirm its bad.