2007 PT Cruiser Shift know area gets really hot

Just the heat coming up from the underside of the vehicle into the shifter boot as there would be a hole in the floor there for the linkage to go threw.

how would I fix this problem?

This is a characteristic of a floor shifter, once the motor and workings get warmed up the heat will rise. I suppose one could try and take apart from on top and put some insulation around in that area, but must be careful not to interfere with any linkages, and where they move as to not get jammed up. Better view from on top that trying to do it from underneath. It is nice in the winter tho...