  We present a study of the performance of endoreversible thermal machines
optimized with respect to the thermodynamic force associated with the cold bath
in the regime of small thermodynamic forces. These thermal machines can work
either as an engine or as a refrigerator. We analyze how the optimal
performances are determined by the dependence of the thermodynamic flux on the
forces. The results are motivated and illustrated with a quantum model, the
three level maser, and explicit analytical expressions of the engine efficiency
as a function of the system parameters are given.
