Tim I know what you mean. I clean my Grandsons PC every 6 months, they have 2 cats.
Back to the OP Sorry! I missed where you said you never run it with the battery inserted, forget what I said about defective battery cells. However there's is one more suggestion I have and worthy of checking, my daughter has an older notebook that was running excessively hot, when I checked the air flow I noticed that the 4 rubber feet
(inserts) were missing, the PC was laying flat on the desktop this was restricting the air flow as the cooling air intake was on the bottom of the notebook. A trip to the hardware store for 4 rubber stick on cabinet door bumpers solved the cooling issue.