Run time=heat=a potential coil issue. You can find cheap aftermarket coils for $12-15 dollars. Not saying you would have to keep a cheap coil on it but it is an inexpensive method to rule out a likely problem. Heat transfer, through poor conductive connections is possible; however, if the heat transfer is THAT extensive you will likely see melted/scorched terminal connections in most if not all situations. Could also be a R/R going out and sending excessive voltage through the system.
What have you verified at this point?
The Goal... All I Need Is The Time...