Stirling engine technologies have been applied to cogeneration systems mainly for residential applications. The performance of Stirling engines has been evaluated considering different operational conditions, which include the electrical and thermal production, working fluid pressure, components geometrical sizing and others. Thermal-economic evaluation represents an effective tool to optimize a power plant with this type of technology. This study presents a mathematical model that encloses the physical variable equations able to simulate the thermodynamic transformations of the cycle, and a set of equations that define the purchase cost of the main plant components. The paper presents a numerical study faithfully simulating a micro-cogeneration unit based on an alpha type Stirling Engine. The simulations were performed through a Mat Lab code able to disclose the best economic output for the best combination of decision variables. Stirling engine performance is affected by geometrical and operational parameters optimization is required in order to obtain the best performance. Results show that the implemented mathematical model reached an optimal solution disclosing a positive profit for the best physical configuration of the system. Also, the cost estimation based on sizing and quality parameters shows a good correlation with the capital investment costs of commercial models.