I have had the same problem with my 3110D, and it got worse last summer. The light would come on and I would disengage the mower and run it at part throttle until it cooled off. The fluid looked like mud. This winter, I drained the fluid and flushed it with water till it ran clear. I could see scale in the radiator tubes through the radiator cap hole. I believe the radiator and engine passages were scaled, which insulates heat transfer. I felt like the engine needed cleaning too. I have never had a lot of luck with consumer grade radiator flush. Being in the A/C business, I see a lot of scaled heat exchangers and scaled ice machines. I poured a pint bottle of nickel safe ice machine cleaner in it and ran it for several hours. Nickel safe ice machine cleaner is inhibited phosphoric acid, which dissolves iron rust and lime or calcium scale. I flushed it real good with clean water and refilled it with a 50/50 mix of water and antifreeze. I read this back in May but didn't want to say anything until it warmed up enough to be able to tell if it made a difference. Now that it has warmed and the grass is growing again, I have put it to the test. We had a week of rain and when it dried up enough to mow the place was a jungle. I really put a load on it, and the light did not come on once.
Anytime you put an aggressive cleaner in your engine you run the risk of breaking something loose that is plugging a hole. Or if something is about to give, the cleaner can finish it off, so if you decide to use a cleaner, keep in mind it can cause a leak. I felt like I had nothing to loose, so I went for it.
Another note, when any engine is run hard then immediately shut off the engine actually gets hotter before it starts to cool off. All the heat has no where to go when the engine is taken from high rpm to stop. It's always a good idea to idle the engine a few minutes with no load to give it a chance to cool before shutting it down. This will extend the life of your engine. When engines run hot, pistons expand. When they cool off, the pistons contract. They can contract more than they expanded. This can cause reduce compression and increase oil consumption.
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