Jerry,
Did you test the starter both in both cold and hot state?
I assume your getting no spark at the coil after it dies?
I haven't tried this on the 944, but have on another car when stranded way out in the boondocks.
Same description, lost spark after it warmed up and then starter no crank, but plenty of voltage in the battery. I ran a hotwire straight from the positive battery to the + post of the coil to bypass the DME and everything that might send an interrupt signal, and since the starter was still frozen, push started the car and to my surprise it actually started! We only ran it like that enough to get home.
I still don't know why, but I ended up replacing the starter and solenoid and it was cured. I guess the ignition circuit was routed through the starter to the coil?