There are several possibilities.
Connection was loose, came apart and shorted to ground.
Too much bare wire and it was exposed out of the nut. Wire flexed and shorted to ground.
Wire caught on sharp metal edge and cut through insulation.

are EMS and the Fire Dept. going to be there tomorrow?

maybe paying out of your teeth isn't such a bad idea after all.

does he also do plastic surgery?

Bare wire ends in the "plastic nut" were not secured to each other tightly enough and when the power came on they started to heat up, which loosened them more, which caused them to arc, which caused them to get hot and develop resistance, and get hotter and start melting the plastic nut, until electricity couldn't flow.

This can often happen because fixtures are often supplied with plastic nuts of the wrong (larger than required) size for the job.
So it is hopefully just a case of trimming back the bit of melted wiring and insulation and repeating the attempt with a new wire nut. Make sure you twist each multistrand wire in the correct direction individually so it is tight and then twist the two wires together so they stay tight while you screw down the wire nut.
Good luck !

Here is a link that might be useful: Youtube wire nut splices

Thanks so far for all your kindness. Would it be helpful to upload a photo of the wires, as we found them after something heated up in there? Pls let me know. we are reading all advice.

A picture is worth a thousand words.

It's a little late for pics. We got the fixture back up and put face plate on, it's been working all day without any explosions so perhaps,this time it is Correctly twined and we used different wire nuts, as post above indicated. Thx again.

I don't think it's late at all. Just becasue it works does not mean it's right.

Just out of curiosity, what field is your husband in?