Optimal configuration of a class of endoreversible heat engines with fixed duration, input energy, and linear phenomenological heat transfer law [q∝Δ(T-1)] has been determined. The optimal cycles that maximize the efficiency and the power output of the engine have been obtained using optimal-control theory, and the differential equations are solved by using Taylor series expansion. It is shown that the optimal cycle for maximum efficiency has eight branches including two isothermal branches, four maximum-efficiency branches, and two adiabatic branches, and that the optimal cycle for maximum-power output has six branches including two isothermal branches, four maximum-power branches, and without an adiabatic branch. The interval of each branch has been obtained, as well as the solutions of the temperatures of heat reservoirs and working fluid. Numerical examples are given. The obtained results are compared with those obtained with Newton’s heat transfer law [q∝Δ(T)] for maximum-efficiency and maximum-power output objectives.