I don't know the answer for sure. Longer alkanes also show a lower autoignition temperature. I believe this is not linked with bond strength nor electron affinity and the like. Some possibilities:
Longer alkanes have more vibration modes and this permits to concentrate more heat on a given atom or bond.
Too short alkanes need a higher temperature to excite the vibration modes.
Longer alkanes have more possibilities to deform into cycles and make aromatic compounds.
I too would be interested in models, interpretations, explanations.