Three common problems with this mower, all which may be causing the hard hot start problem. One, this engine likes to over heat due to grass collecting around the cylinder. Two, carb mounting bolts loosen up. Three, carb jets plug easily. Overheating might be causing the coil to breakdown when sitting with no air flow. Loose bolts may be creating a lean hot starting mixture. Partially plugged main jet again may cause a lean hot mixture. If it came into the shop I would start by removing the shroud and make sure the cooling fins are clean and at the same time I would check the carb bolts. Reinstall the shroud and run the unit until hot. Shut down wait three minutes and try starting. If no start, I would check for spark, if I had spark I would go after the carb. I would remove the carb, clean and rebuild with new float needle and seat. If no spark I would replace the coil and repeat the test.
