Wires usually burn solidly from the point of short to the point the wire changes size. The exception to this is where high current circuits have bad connections. In the case of a bad connection the connection itself increases the current and causes localized heating. Most temp sensors are low current sensing devices and can't draw any current due to the internal circuitry of the control unit monitoring them.
In the case of temp switches they are current carriers and the way you describe yours, I believe that the connections themselves were the problem. Check the circuit with an ammeter and verify that consumption is less than recommended fuse rating. If in doubt install an inline fuse of smaller rating in a strategic location.
Bosch Master, ASE Master, L1
33 years MB technician