Any time an electrical connection gets hot, it's because there's some resistance there. Current flowing through a resistance creates heat. You can verify this with a digital voltmeter. Switch it to one of the lowest DC voltage ranges, then place one probe on the battery post, and the other probe on the cable clamp. Ideally, with the engine running, you should find 0.0 volts. The same is true when a helper cranks the engine, but in reality, you're allowed up to 0.2 volts across any one mechanical connection when that high current is trying to flow. If you find more than that, take that connection apart and clean and tighten it.
Even with that bad connection, the generator should have kept the engine running. At most the battery should have failed to be recharged and it wouldn't have cranked the engine next time. Do you have the results of the generator tests? If you do, please list the full-load output current and the "ripple" voltage.
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Thursday, April 30th, 2015 AT 8:21 PM