Starter turns over slowly when hot
 

First thing in the morning, the starter turns over perfectly, but once the car is hot, the starter initially turns very slowly for a moment, almost like its not going to turn at all. and then goes at normal speed. I was reading in the Rennlist 996 forum that the problem in 911s is a cable going to the starter that doesn't provide enough juice and needs to be replaced according to a TSB. Battery is good, dead cold voltage after sitting overnight is 12.55v

Does the Boxster have the same problem?

The first thing I would do is clean and check all the battery connectors including the ends that bolt to the chassis and starter to make sure there is no corrosion and they are making a good connection.

Edit: I had a car with a starter that had worn out brushes, that exhibited the same symptoms.

I had a car that experienced this same problem, ended up being a worn out starter.
The windings in the motor seem to weaken when hot..

I would check all the obvious first, you can get you battery load tested to see if the batteries failing.
I went through all that stuff first..
T

Really it could be any of the three main components; battery, battery cables, or starter. They can all give the same symptoms. I'd start with the easy and cheap parts first (have the battery load tested and clean and tighten the battery cables) and then go further if the problem isn't resolved.

First thing in the morning, the starter turns over perfectly

Then it's not the cables or connections, it's the starter or a related component.