We analyze the thermodynamics of a simple heat engine. The engine’s efficiency is calculated for an idealized but reasonable model. The engine’s work cycle is compared with a Carnot cycle, and it is shown to be equivalent to the Carnot cycle as an extremely ideal limiting case. A working model of the engine is easily constructed for classroom demonstrations. We measured the force law parameters for a working model, and we estimate the efficiency of this model. The estimated efficiency of our demonstration engine is small compared with that of a Carnot engine operating at the same temperatures. We show that a Carnot engine could in principle be constructed based on the thermal expansion concept, but its efficiency would be intrinsically small when rubber is the working substance because of the inherently small incremental temperature increase possible in an adiabatic expansion.