Probable silly question from a newbie here, but is it normal for the shifter plate to be very warm to the touch while operating in typical road use (60MPH on flat highway) in normal ambient temperatures (75 to 80F)? I just want to be sure there isn't an underlying issue, but I didn't find any threads about it.

Thanks,

 

Tell us what country you are in !!!

Suggest you get underneath and look if any heat shields etc have been removed above the gearbox.
Have a look at this post for a photo...

Floor pan heat shield - Jaguar Forums - Jaguar Enthusiasts Forum