A dynamic model of a concentrating solar thermal array and thermal energy storage system is presented that is differentiable in the design decision variables: solar aperture area and thermal energy storage capacity. The model takes as input the geographic location of the system of interest and the corresponding discrete hourly solar insolation data, and calculates the annual thermal and economic performance of a particular design. The model is formulated for use in determining optimal hybridization strategies for industrial process heat applications using deterministic gradient-based optimization algorithms. Both convex and nonconvex problem formulations are presented. To demonstrate the practicability of the models, they were applied to four different case studies for three disparate geographic locations in the US. The corresponding optimal design problems were solved to global optimality using deterministic gradient-based optimization algorithms. The model and optimization-based analysis provide a rigorous quantitative design and investment decision-making framework for engineering design and project investment workflows.