Analysis of irreversible heat engines, which operate between two variable temperature heat reservoirs, has been performed by means of the second law of thermodynamics. The results show that the optimal balancing between the sizes of the heat exchangers at the hot and cold ends of the engine is affected by the ratio E (or E'). Also, the maximum power output of the engine varies significantly with E (or E'). Conversely, the efficiency at the maximum power point does not depend on E (or E'). The optimal temperature ratio across the inner compartment of the heat engine depends on the inlet temperatures to the heat exchangers,