Engine Ariens 2010 19.5 HP engine issues

[68_GS_400]

Son in Law's Ariens mower s/n 93604800 purchased in 2010 is having issues. His battery went dead and he bought one from big box store to replace it. Battery terminals were reversed but he did not notice that and burned out the starter and solenoid. I replaced both and got it running fairly well. (I have JD 100 series with same basic engine and used it to get choke / throttle setting close to being right.)
He now says it 'overheats'. He can mow for 1/2 hr. but no more. Engine stalls and he must push to shed and run fans over it. I'm not sure that is issue for it runs fine up to the point of stalling.
Where do I start in troubleshooting this issue? I don't know that overheating is the issue since the engine fins are clear, all body parts are in place and oil level is correct. My thought is for some reason the fuel mixture is wrong and causing the problem. Fuel filter and spark plug were changed at beginning of this season. I don't want to start making adjustments without having a plan as to where I am heading or what I should be changing.
(BTW - my SIL has limited mechanical ability, lives about 10 mile away, and works irregular hours so working with him on this is difficult. I want to have some definite idea as to problem and solution when I go up there to repair things and to be sure I have right tools with me when I go.)

 

[mechanic mark]

Enter your model & serial numbers then click on service manual and go to troubleshooting section.

Ariens Order Owners Manuals

Check air filter for replacement.

 

[Deerlane]

Have a extra spark plug in your pocket and go mow. When the tractor shuts off, unplug the wire from the engines plug and install your pocket plug and ground it. Crank over engine to see if you have spark.
A bad mod coil will expand the wires inside, that you cant see. There is a ground wire that's goes to a coil to shut down the spark. It may have some damage from a + ground.