A heat engine employs an auxiliary cylinder to receiving exhaust gases from a main cylinder during its exhaust phase to extract mechanical energy from the heat in the exhaust gases. The auxiliary cylinder has an auxiliary piston that reciprocates with an asymmetric pattern in respect to the main crank a counter-rotating auxiliary cranks such that the downward stroke of the auxiliary piston and the upward stroke of the auxiliary piston correspond to crank angles above and below 180 degrees. In one favorable embodiment, fresh air can be drawn in and combined with the exhaust gases.