Holy Smokes. I had the same complaint about a month ago. I noticed it coming from the same place (auto shifter) after I put in the radio. I opened the dash back up, in the radio area, and looked around but all the carpets and insulation were in place. My guess for the heat is the typical 7m hot as hades under hood temps heat up the firewall and underside as the under hood air vents out of the bottom of the car.
One thing did help. Not necessarily from the shifter heat but heat in general. I made sure that my ac was not venting from the outside. I put it on recirculate cabin air and that seemed to help as well as not blowing the air through the floor or bottom vent settings. My feet and legs were sweating from the auto ac fan setting mixing the air from the outside and pushing it through the bottom and top vents as well.
One more thought I had was the fact that I removed the gasket that goes in between the back of the firewall and the engine hood. I read somewhere it would help vent the heat out of the engine compartment. As you know the fresh air intake for the ac runs along or under the wipers / front windshield and maybe the heated air was being sucked in.
