Can't speak to the 02s but my 01 Classic and the rental Softails (00 & 01) with EFI I've ridden have all been leg warmers when gridlocked in traffic (southeast US 95 degree days) but nothing that would cause a blister. Mine has no oil cooler and neither did the rentals. About the only driveability issue has been pinging at low rpm <1500 and a grabby clutch (only when real hot). Out on the open road my wife says the ride is much cooler for her when my feet are up on the hiway pegs but that doesn't help in traffic.
I'm with Hippo on this one - it's gonna end up being something weird and more likely a combo of small things than one big problem. It will take a lot of patience on your part and a dealer mechanic who is willing to invest the time to duplicate the condition and make a proper diagnosis. Unfortunately for you, those guys are usually paid flat rate and after a couple of hours have to book some regular work to feed their kids. Good luck!
I'm with Hippo on this one - it's gonna end up being something weird and more likely a combo of small things than one big problem. It will take a lot of patience on your part and a dealer mechanic who is willing to invest the time to duplicate the condition and make a proper diagnosis. Unfortunately for you, those guys are usually paid flat rate and after a couple of hours have to book some regular work to feed their kids. Good luck!