On 25/08/2015 16:16, NY wrote:

Or are you saying that some engines injected fuel into cool air during
the induction stroke, then compressed the fuel-and-air mixture (as
opposed to just the air) and let combustion occur when the air had been
compressed to a high enough temperature?

There are engines like that.
I once had a two stroke compression ignition engine that did that.
Used to drive a six inch prop.