  We investigate generic heat engines and refrigerators operating between two
heat reservoirs, for the condition when their efficiencies are equal to each
other. It is shown that the corresponding value of efficiency is given as the
inverse of the generalized golden mean, $\phi_p$, where the parameter $p$
depends on the degree of irreversibility of both engine and refrigerator. The
reversible case ($p=1$) yields the efficiency in terms of the standard golden
mean. We also extend the analysis to a three-heat-resrervoir setup.
