These things are a little hard to diagnose sometimes, once the car has started - if you turn it off before it gets warm and try and start it again, does it start straight up?
One thing to look for is after it's been sat for a while, take the top of the carb off and look into the float chamber and verify that there's still fuel in the carb after it's been sat (you can do this with the carb in situ, just don't drop anything into it). It could be that fuel is very slowly leaking from the carb, so little that it's hardly noticeable - but left a while it empties. Then you crank the engine, fuel pump supplies fresh fuel OK until the carb is full enough to start working. If the float is at the top then it's good, if the float is near the bottom of the chamber then you have a leak.
Does it turn over quite quickly while you're starting it? Even with a good battery, if the starter motor is tired then it might struggle to turn it fast enough?
Rob Amos
Happiness is a stock VW