Check to see that it sin't leaking air into the engine when hot. Top split engines to have a nasty tendency to leak around the join when old and hot. Usually this manifest itself with burning oil, a favourite GT500 trick after 15,000 miles or so.
Or it could be like an engine I had to rebuild because the previous owner didn't quite understand why silicon sealant is used during rebuilds. Yep, it sucked in air and blew out oil when hot plus was a !"£%^% to start when hot.
The rebuild was done wrong as well because a clutch bearing was in all wrong, causing it to friction weld a gear onto the layshaft.
GT500 engines are nice to rebuild and the Clymer Manual show how to do it in detail.
If you're having hot starting problems, check the oil level and check if the exhaust smells of gear oil.
If so, then check the torque settings of the crank case bolts. If that doesn't solve the problem then the engine will need cracking open and the cases resealed with generous amounts of silcon rubber sealant.
Smearing the silicon sealant during a rebuild is another reason some engines don't seal properly.
However it could just need new rings, so check the compression first. Japanese strokers were never very high on compression when new, so wear and age can drop this further.
Old strokers can be a real pain sometimes when it comes to starting.
However the general rule is that a fast two stroke will always be a bad starter. Good starters are always the slower than average ones.