Small Engines (Lawn Mowers, etc.): engine overheating, small engine warehouse, snapper rider

Question
I replaced a blown engine on a a 1991 Snapper rear engine Model 3312X6S rider. The original engine was a:
1) 12hp B&S model 281707
           Type  0162-01
           Code  88082431
I called Small Engine Warehouse and ordered the engine they recommended to replace it. The replacement engine was a 2) B&S 13.5 HP Model- 28R707
              Type   1120-E1
              Code-  030531ZE
It came with an electric starter.
When it arrived the only change I made was to place a recoil starter on top of the crank. I reused the muffler off the old engine. I matched up the drive disk to the transmission and filled it to level with Penzoil 30W. It ran fine. Initial run time was about 20 minutes. I shut down and noticed the block was extremely hot this included the base and the frame of the mower. I have not encountered this type of heat on my 9hp B&S on another Snapper rider even after a couple of hours run time. I dont beleieve the engine suffered any damage but I am concerned it will if i ran it longer. The engine oil does not appear to be burned. The mower ran fine in all gears and it does not appear that the engine was bogged down due to any type of friction from the disk drive on the Snapper transmission. This is the third re engine job on various Snapper riders I have owned over 20 years so I feel fairly mechanically competetnt on these units. Just wondering if I'm missing something. I'm Stumped.
PS- I didnt monkey with the flywheel just removed the shroud to thread the adapter shaft into the crank end to accept the recoil starter. Screen replaced and no binding seen or heard.

Answer
Glad you mentioned the flywheel...I would have assumed the cooling fins may have been different.

Is the engine RPM, high speed, correct.  Since you have have some experience I'm sure you can tell just by ear.

Are there any adjustments on the carb that could lean the air/fuel mix?  The parts diagram shows an idle air/fuel mix needle.
What spark plug is in the engine?  I'm guessing a J19LM gapped at .030.

Let me know.
Eric