Beyond a certain point that is certainly true. However, if you are injecting more fuel into the head in the first place, that will increase temperature. Running it rich will also increase temperature UNTIL so much fuel is coming in that it no longer combusts efficiently and then you start to "coke" the head and foul the plug... at which point it cools down as combustion is affected. So if the plug isn't fouling but you're running rich, then you may be adding heat to the equation, not cooling it.
At least, that is my understanding.
These aircooled heads run hot. I would definitely move to synth oil as soon as possible (after break-in). and as I said earlier, one easy and non-invasive way of keeping tabs on the issue is to check oil temperature or head temperature.
Cheap way: meat thermometer in dipstick. Look for threads on that; it's been done.
Other ways: a head temp meter is an easy install, requiring only that a sensor be placed under a bolt head or spark plug (decomp valve might also work). Dakota digital and others sell them. Under the spark plug is the worst placement.. it gives an inaccurate view as it is the very hottest place on an engine.
An oil temp sensor could also be installed somewhere I'm sure.
I use both an oil temp meter and a head temp meter on my diesel; but that is really because in building the diesel I was in unknown territory and was looking to get maximum efficiency out of the engine and wanted to make sure it didn't overheat. As it turned out, the highly-modified diesel runs much cooler than the gas engine ever did, so it hasn't been a problem; I'll probably remove them for my long distance ride just to keep weight down.
From what I read on the oil cooler threads, I think that they seemed more effort than they were worth - and possibly dangerous if a blockage occured.
So I would use synth oil, and maybe back off a bit on your fuel settings and see if that helps.