Solar energy integration in heat consuming processes is a promising replacement for fossil energy. We are interested in a small Solar Parabolic Trough Collectors field combined with a sensible heat storage reservoir. Unfortunately, such a system has a higher cost than fossil energy and is challenging to optimize. Therefore, this work's main objective is to provide an optimized design and management to minimize energy cost (EC) and maximize renewable energy utilization fraction (REF). This study is done by optimizing the sizing and the thermal energy flow management of a hybrid solar-fossil fuel energy system. The optimization problem is formulated based on mass and energy conservation equations, heat transfer phenomena modeling, correlations, and economic data. We resolved it by combining trial and error method, multi-node calculation procedure, and genetic algorithm. To evaluate our method, we studied a hybrid solar-fossil fuel energy system used for the bitumen heat maintaining process in Rabat region-Morocco. The evaluation considered different thermal storage capacities. Using our optimization, we reached REF >= 40% and EC < 0.05US$/kWh for small thermal capacities and REF >= 85% and EC less than 0.2US$/kWh for large thermal capacities. This is equivalent to saving, respectively, more than 0.75 and 1.5 tons of CO2 emissions/year/kW for small and large thermal storage capacities. Other important recommendations are also provided in this work.