You know, I hear a lot of people say this but I have always broke my engines in on a stand and they have never overheated. But I suppose if one let it set at idle for a long period it would. I don't do that, I bring them up to around 200°, run for 30 seconds at mid rpm, back to idle for about 10 secs, then mid rpm again, do this 3-4 time's then shut it down and let it cool off, then repeat until a gallon is burned. Then I tune it best one can on the ground, put it in an airframe and go fly. Usually after some flying some fine tuning is needed.
Gasoline engines have zero cooling from the fuel, unlike glow/nitro engines, so break-in is exceptionally hard on the engines. The only way to ensure adequate cooling is to actually fly the engine- no harm will ever be done to a brand spanking new gasoline engine if it is flown within its first 10 minutes of run time. What you want to do is heat cycle the engine, which running on the ground is ineffective at. 200F is fairly cool, you want it nearing 300F at WOT to help the rings seat well, otherwise it will either take longer for them to seat, or you may just wind up doing damage to the rings themselves. A lot of us from the glow days are so used to running the engines on the ground to break them in that it's hard to break the habit on gasoline engines, but gasoline engines are a totally different beast and have to be ran in differently.
As described to me by, well, pretty much everyone at Desert Aircraft (who, by the way, all gasoline engines are compared to), you want to bolt the engine to the airplane, start it and check your needle settings to ensure it will run on the rich side, and will maintain an idle. Once it does this on the ground, fly it. Do lots of uplines and downlines. If you get bored of just going hammerheads then mix in IMAC aerobatics. The full throttle/heating and idle/cooling is what helps the rings to set properly in a short amount of time. All 3 of my DA's and my ZDZ180 I've done this with and all of them ran like scalded apes
Total run time on the ground for each engine was roughly 2 minutes or less.