Cheap mantle thermo-probe fix?

Probably. Certainly if it’s a thermocouple. With a RTD or thermistor you need the bit at the end. With a thermocouple, the magic is in the wires themselves.

Simply put, if you succeed in making a clean bond between the two wires and the bond experiences the measured temperature uniformly, then it doesn’t matter what incidental metals are involved. Thus twisting, welding, soldering, crimping - they all work, until… Until corrosion sets in between the connections. Thus, twisting is the least preferable over time because the metal is neither fused nor crushed together sufficiently to form what’s termed “a gas tight connection.” That said, almost every experiment I ever run used twisted connections because it is easy.

Reference: Okay to twist thermocouple wires?

To quote @Beaker