Kawasaki FH53 in J.D. 325, only fires on one cylinder when I restart it after it was shut off when warmed up. Sometimes takes a few minutes to kick in. Always starts and fires on both when it is cold. Also, alternator light has been on for about 25 hours, the battery is apparently charging as it has never been dead or weak.

Any help will be appreciated.

It's likely that one of your ignition coils is breaking down when hot, Kawasaki recommends replacing both at the same time. I have had good luck just replacing the bad one, but thats up to you.

If you have been running with the electric pto engaged then the alternator is probably working, if you have not been using the electric pto, then 25 hours of run time will not affect the battery all that much as the engine uses little if any battery power to run.