In my field of work as a chemical plant operator we feed what we call a synthensis gas generator pure O2 and methane. The generator is preheated to above 1000 deg C prior to the introduction of the O2, methane feed so that auto ignition takes place. The result of the reaction of the methane and 02 is a Carbon Monoxide/ Hydogen gas mixture. The generator runs about 1350 degrees C when it's operated properly. To control the temp of the generator we limit the amount of O2 we feed it by monitoring what we call the methane slip, which is the amount of unburned/unreacted methane left in the system after the reaction of methane and O2 takes place. If we were to feed too much O2 the reaction in the system would start making CO2, carbon dioxide instead of CO. The CO2 reaction produces a whole lot more heat than the CO reaction, if we fed too much O2 for even just a few seconds we could have a melt down on our generator.
My point here is really combustion is a reaction between oxygen and a hydrocarbon that requires an ignition source that produces pressure and heat. The more O2 the hotter the reaction will be because of the production of CO2 a much hotter reaction. If you run too rich then you won't react the Carbon to CO and then you end up with a bunch of soot or carbon build up in the system.
I also argree that in a internal combustion engine you need a certain amount of excess fuel for cooling purposes.
I am no scientist and maybe someone who can explain this better to me.