Before you toss it to the dealer...... it sounds like water pump is fine b/c you aren't overheating while operating but rather it's leaking out after shut down (a true sign of air trapped, bad cap or possibly pump). If the tank and trunk aren't wet, that's a good sign there aren't any leaks. So couple of things to check before you give up and brace yourself for an expensive fix..... (in order BTW)
First off, let the vehicle cool down completely (overnight suggested). Then, using a flashlight, carefully check the coolant level. The Porsche coolant (mixed w/ 50% distilled water) is extremely difficult to read accurately via the tank guage w/out a flashlight. If it's over full, use a turkey baster to suck some out. In total, the system holds 18 liters IIRC.
Next, check the bleeder valve and o-rings. They are known to go bad. (info in archives on how to access which you'll need for step below anyhow). If lot's of residue around valve - that's most likely source of problem or could just need bled.
Now make sure the system is air free by properly bleeding it. (directions are in the archives - takes about 30 min to do). Short cut method, but not 100% gtd effective, is to open the bleeder valve (and leave open) and drive around w/ some random accelerations, upto 5K RPM, for about 15min. close valve and test her out). This will be when you'll check to make sure both radiator fans are working as well, but again since no overheat issue while driving, sounds like you're ok there.
Hopefully you've found the no cost (bleeder valve will cost though) problem. If not, these things will definitely cost $ to diagnose....
Take to indy for a quick pressure test on entire system (about 1hr). You need to find a shop that has the special adapter to fit the Porsche coolant tank.
Yes, you have the updated cap but it could still be defective..... might be worth picking up a new one ~ $15-20 (even at dealer)
If none of this helps then most likely you'll need to have someone check the water pump to make sure it's working. You didn't say, not that I saw at least, how many miles are on your '02. My guess is w/ under 75K water pump should be good so you hopefully will find your answer in one of the above no cost options.
Good luck and let us know the results.
