The heat transfer equations and best engineering practices haven't changed for over 70 years. You can't fool physics. Thinner fins is not anywhere near as important as total surface area. Look at the radiator on your car, the fins are thin to increase the total surface area by using more fins. Thinner and leaving out half the fins is of no advantage to cooling. And yes, aluminum cylinders with plated bores are much more efficient at transfering heat than a steel sleeve. Thermal conductivity of aluminum is much higher than iron. Thermal conductivity closely parallels electrical conductivity. Copper is a better thermal conductor than aluminum which are much better than iron.

To be certain, I know of no cooling problems with the BME - no experience with it.