Looking at your picture, It also looks as if there is enough room to get on the wrong side of the actual connector - i.e., the hole looks larger than the pin inside. Hit the pin inside, you're golden. Hit beside the connector, you'll have initial connection - not tight - heat builds, oxidation increases, resistance increases, heat increases till you get what you describe.
As sharp and precise as we think the German engineers are, their accountants seem to have the sharper pencil. Every BMW M/C (prior to LED and Zenon) has undersized headlight wiring. It's a laugh. But saves money. (and fits better within handlebars) In the relatively short wiring on M/C, the wiring produces about a volt of drop to the headlights - dimming them as one would expect. Pop in higher watt bulbs, and connectors and/or switchgear melt on a regular basis. Most owners feed a large wire from the batt and use the headlight switch gear to trip a relay - and rewire from the relay to the headlamp. Brighter headlights, and no fuss with switchgear or connectors.
So, Vince is spot on. Stock wiring is barely up to the job. A German thing. Anything but a tight, clean connection will cause the type of heat necessary to melt the connector.
frank