Engine temperature effect on efficiency is about heat loss, which isn't accounted for in the Carnot cycle (it assumes perfectly reversible cycle, and heat conduction across a temperature difference is not reversible: it's heat bleeding from one point to another and averaging out, kind of like mixing two substances).

If the metal walls of your combustion chamber are cold, there will be more heat transferred and more entropy generated. Looking more physically, heat lost after combustion reduces the temperature and therefore pressure of the gas on the power stroke, reducing power output for a given heat input (i.e. less efficient).