The V8 is known for having a somewhat marginal cooling system even when in 1st class nick. It's important therefore to attend to the rest of the cooling system whilst your at it!
Make sure you give the whole sytem a good flushing with a proprietory flushing agent that's suitable for aluminium engines.
Back flush the heater matrix by disconnecting the hoses from the heater and then coupling it up to a hosepipe (keeps yopu nice and warm in winter after this!).
As far as possible renew all the hoses in case any have collapsed internally and are blocking the flow.
Change the thermostat.
Change the radiator pressure cap.
Check that the water pump is working - my method is to (breifly!) run the engine with the radiator off and the pump inlet and outlet open and pour some water in. If you don't get drenched by the pump throwing it back out you need to look more closely at the pump.
It is known for the coolant passages in the inlet manifold to "jelly" up. If in doubt take it off (surprisingly easy) and flush it out off the engine.
Now we are on to the radiator! And yes you will need a P6 specific radiator. There are a number of variations.
Automatics have a transmission oil "cooler" which consists of a length of copper pipe layed in the side tank of the radiator with hose connections at each end. This serves to heat up the transmission oil quickly when everything's cold and then to cool it when everything's up to temperature. It significantly impairs engine cooling capacity. If you feel so inclined you could disconnect it (you can leave it in situ without problem) and substitute it with a separate oil cooler.
3500S's have a similar radiator without the transmission oil cooler.
Either radiator can be recorred with a thicker core - three row instead of 2 row - that's much better. (the core is all the fins and tubes between the two tanks)
Baspoke aluminium radaitors are availabele from Alan Ransbottom at Leighton Buzzard.
Another worthwhile mod to do at the same time is to fit a radiator header tank. Any old one will do from your local scrapyard. The former overflow pipe now goes to the header tank, the readiator cap is replaced by a blanking cap and the pressure cap goes on the header tank. This makes sure the coolant level always covers all of the cooling fins in the radiator.
Finally you might be well advised to fit an electric fan, either as well as or instead of the standard engine driven fan.
There's no need to source a replacement readiator, you should find radiator repair firms in your local yellow pages and they will be able to recore your existing rad, either as standard or with a thicker three row core.
Hope that wasn't too scary
Chris