The 12V cig lighter type plugs generally get hot because of a bad or dirty connection. The quality control on the male plugs appears to be very poor and some are too large and some too small to fit the hole and hence do not make good contact primarily on the tip end. This causes a high resistance connection and heat. If you don't want to replace the plug and socket with something better, keep the tip clean and make sure the plug is in all the way and tight. If the plug is too small to stay firmly in place, a toothpick can be used to wedge it in.
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