This question should be in the homeimprovement category but I am also a home improvement expert.
First step is to verify both ends of the wires are good and clean. Next step is to make sure the wires are good and wraped tights before wire nutting. Now if it still burns up then your cook top element has an internal short causing high resistance and the resistance is going to heat up in the weakest link which is the wire connection.
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The reason your wire nuts burned off is because of the extreme heat that is produced by your flat top grill. The wire nuts are only plastic - so any heat will melt them. What you need to do is get ceramic wire nuts. These are rated for extreme heat. Or you will need to connect the wires using small split bolts and sealing it with rubber tape. Once your connections are tight and re-done the way I state, it will be fine.
Now the other thing is - you need to make sure the wiring is the proper size. If your wire is too small, it will cause overheating as well. 30amps should have #10 wire, 50amps should have #8 wire. Both wire sizes will be copper.
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