Detailed performance analysis for a thermal system using a generalized irreversible solar-driven heat engine model is performed. The heat engine (HE) model is formed by the first and the second laws of thermodynamics and economical considerations. Also, the HE is optimized under the thermo-economic objective function (TEOF), power output, and overall efficiency criteria. The TEOF is used to evaluate the investment, including lost exergy, and operating and maintenance costs together. It is defined as the power output per unit total cost. In the HE model, investment and operating and maintenance costs are regarded as proportional to the power output of the heat engine, while lost exergy cost is regarded as proportional to the entropy generation rate. In thermal system designs, various scenarios are considered regarding size and configuration limits. To fulfill the requirements, performance output parameters can be evaluated with weighing factors. In the HE model, the hot surface heat transfer mechanisms are considered as both radiation and convection, but the cold surface heat transfer mechanism is considered as convection, only. Also, the thermo-economic performance is evaluated considering heat losses. Besides overall efficiency and operational temperatures of the hot working fluid have been discoursed in detail. HE model performance data and optimized results are computed numerically. And finally, an artificial neural network model is presented for an alternative solution to compute HE performance data with less effort and less input data.