I want to throw in a TDI experience here that should be considered an "outlier" but cleared up a hard start problem (when cold and warm, but worse when warm.) It turned out to be a replacement of the clutch assembly (flywheel, clutch, etc.) The foreshadow that was ignored was a low clutch pedal, (grabbing about 1/2" off the floor) and, when started while depressing clutch pedal in any gear, the engine would turn over a little slow and gain speed over about 8 seconds - then start. Upon starting if you listened really close, you could hear what sounded like the starter hanging up for a second or two (old school bendix noise). Also, when car was idling, depressing the clutch to put car in gear would also change pitch of engine (as though it were under a load - dropping rpms noticably.) Again, this was an exception, but wanted to add it since I checked all other avenues first (Relay 109, starter, static and VAG-Com Timing, battery load test, alternator output.....) Just something to keep in mind if all else has checked out.
After the replacement of clutch assembly, car starts instantaneous hot or cold.
And even though it was a lot of pre checks and post checks, there is a piece of mind knowing all of the other items are in good shape.
Just for the record, this was on a 1999 Beetle TDI with approx. 93,000 city miles...