Jim, transponder right behind the firewall in the center is not a good idea. It will be exactly aft in the middle of the tail exhaust pipes.
I installed mine (RAMI shark fin antenna: no problems for maintenance, since it has 2 connection with the skin and the coax connection) between the pilot pedals, just beside the longeron and now that I installed lower cowl and exhaust I am scratching my head if that is the ideal installation. It would have been better if it was 4'' apart on the left, so to clear more the aft exhaust tail pipe. I am not worried very much about heat (I will add a heat shield on the pipe) but about signal shadow.
My last idea - untile next ;-) - is to use such antenna for DME and installing the other identical antenna under the belly, under the baggage compartment.
In my case I have problems to install everything in the rear, because I have 1 COMM, 1 ADF, 1 XNDR, 1 DME under the belly and the latters should stay 6' apart one from the other, XNDR antenna 3' from receiver, COMM from ADF (if I well recall) 3' and so on...
On the other side, I saw a few airplanes with a XNDR installation like mine (between pedals) and they did not report issues. Maybe, you can try to locate it slightly on the left, behind of the left pilot pedal ot on its left. Double check if it is necessary to have a 12'X12' square flat surface. I can't remember now.
Hope this helps (and hope someone also clarifies the situation to me).
Camillo