What is a good melting point for a lithium battery contact fuse?
TL;DR - a current-based solution is probably the only workable one in this case, though thermal cuttoff migh be useful and is often implemented, it doesn't work exactly like a fuse.

As mentioned by the users commenting on your question, lithium-based batteries, including the cylindrical 18650 Li-Ions in the Tesla that you mention, become hugely dangerous at high temperatures. An overheated charged battery migh burst, spraying its insides everywhere, start burning ferociously, or both. Google "lipo explosion". Because of this, most responsible designs employ an electronic circuit called the Power Control Module, or PCM, which protects the battery from overcharging, overdischarging, reverse polarisation of the charger and sometimes overheating, requiring a separate thermistor. Keep in mind that this PCM module is not "welded" into the battery but usually attached with Kapton tape (Li-Po) or hidden beneath the sheath of the cylinder (Li-Ion). It is wired in series with the load and you might of it like a smart fuse.

In high-current devices, like drones, there is a risk of overheating because of the device drawing a multitude of the battery's capacity (sometimes 40x or more) from the battery bank. Therefore you sometimes find a thermistor attached to the battery control module and put between the cells - though it does not work like a circuit breaker, think of it more like of a peripheral sensor for the control module. And it's definitely not going in series with the load, at least in no application I know.