Why would an electric baseboard heater burn the wire connector off the black wires?
The wire nut burned because the connection was not sound. May have been the nut was loose or the wires not paired/lined up cleanly and properly. Either way, this creates a very high resistance connection that can create a LOT of heat under load, and an 8' heater is a pretty good load, typically 250 watts per foot. This resistance is not seen as any extra amperage by the circuit so the breaker does not know anything is wrong.

This problem was not the fault of the heater, it was the poor connection.

The ticking can be typical with baseboard heaters. It's the metal expanding and contracting.