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Ignoring other issues with inline thermistors, all the damage I've seen indicates the issue isn't too little resistance (cables melting from overamperage) but too much -- contact pins mate poorly, and thus become victim to (I^2)r. A 50cm, 12A wire with 20 mOhm resistance can dissipate 3 watts along its entire length , but if that power is all focused on a portion of one pin contact, the surrounding plastic will melt.
Yes, which is why you'd use a PTC thermistor (which increases resistance as temperature increases) instead of the more commonly found NTC thermistor (which reduces resistance as temperature increases), although, I don't know if they can be used to say, cut off the supply entirely. It's probably not possible, and I certainly did not take these other considerations into account - it's just something I've been wondering.