John;
Melted electrical connectors, unless subjected to an external heat source (like an under-hood fire) are inevitably a result of an in-line resistance cause by corrosion or looseness or some combination of the two, resulting in heating due to (ohms Law derivative) I2R. Where I is the current in the circuit, squared, times the in-line resistance (which should have ideally been MUCH lower). Since there was no report of a fire, or fuse blowing (due to excessive current, more than normal) I can reasonably make this deduction...
My advice to Fran is to replace damaged connector (and the heat-damaged areas are the forensic evidence and clue as to the precise location of heat-source/poor connection!), properly crimping terminals onto wires (using ACZP on stripped wires to create the next best thing to a soldered Gas-Tight-Joint (if it was me, I'd solder newly stripped wire ends into the pins!), and remate the connector (if a two part separable type) with ACZP on mating surfaces.
References:
ACZP: http://www.sw-em.com/anti_corrosive_paste.htm
Crimping: http://www.sw-em.com/Wiring%20Notes.htm#Crimp_terminals_Tools_and_making_a_Proper_Crimp
Connectors shown on ES Wiring Diagram ( http://www.sw-em.com/1800ES%20Wiring%20Diagram.jpg ) are not like the Hex Conns used on the 122, but info here might be useful: http://www.sw-em.com/voltage_drop_in_headlights_power_in_hex_connector.htm
Cheers
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