The autoignition temperature of a gasoline/air mixture depends upon a lot of variables. Most importantly, what is the air/fuel mixture (equivalence) ratio? What is the ambient pressure? Is the mixture homogeneous or stratified? Iso-octane reference fuel will auto-ignite at stoichiometric, 1 atm conditions at about 600degC. Lean air/fuel mixtures are notoriously difficult to ignite.
The charge temperature in the expansion chamber of a loop-scavenged two-stroke engine is likely far less than 1300degF, due to the mixing of the cool intake scavenge flow with the trailing end of the exhaust flow, prior to the acoustic reversion pressure wave driving them back into the cylinder.
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