Indirectly or externally fired gas turbines (IFGT or EFGT) are interesting technologies under development for small and medium scale combined heat and power (CHP) supplies in combination with micro gas turbine technologies. The emphasis is primarily on the utilization of the waste heat from the turbine in a recuperative process and the possibility of burning biomass even "dirty" fuel by employing a high temperature heat exchanger (HTHE) to avoid the combustion gases passing through the turbine. In this paper, finite time thermodynamics is employed in the performance analysis of a class of irreversible closed IFGT cycles coupled to variable temperature heat reservoirs. Based on the derived analytical formulae for the dimensionless power output and efficiency, the efficiency optimization is performed in two aspects. The first is to search the optimum heat conductance distribution corresponding to the efficiency optimization among the hot- and cold-side of the heat reservoirs and the high temperature heat exchangers for a fixed total heat exchanger inventory. The second is to search the optimum thermal capacitance rate matching corresponding to the maximum efficiency between the working fluid and the high-temperature heat reservoir for a fixed ratio of the thermal capacitance rates of the two heat reservoirs. The influences of some design parameters on the optimum heat conductance distribution, the optimum thermal capacitance rate matching and the maximum power output, which include the inlet temperature ratio of the two heat reservoirs, the efficiencies of the compressor and the gas turbine, and the total pressure recovery coefficient, are provided by numerical examples. The power plant configuration under optimized operation condition leads to a smaller size, including the compressor, turbine, two heat reservoirs and the HTHE.