This study aims to assess for a Stirling engine the influence of the overall heat transfer coefficient variation on the optimum state and on the optimum distribution of the heat transfer surface conductance or area among the machine heat exchangers. The analysis is based on a Stifling machine optimization method, previously elaborated, which is now applied to a cycle with total heat regeneration. The method was conceived for an irreversible cycle with heat transfer across temperature differences at the source and the sink, and heat losses between the hot-end and the cold-end of the engine. Source and sink of finite thermal capacity as well as thermostats are considered. The new approach considers a linear variation of the overall heat transfer coefficient of the machine heat exchangers with respect to the local temperature difference. A comparison of the optimum state and the optimum distribution of the heat transfer surface conductance or area among the heater and the cooler is made for several cases.