With easier access to space and the growing integration of power-dense components, small-scale thermal management solutions are increasingly in demand for small satellite systems. Due to the strict mass and volume requirements commanded by such power-dense small spacecraft, heat pipes with thin and flat architectures provide nearly ideal solutions for the efficient transfer and dissipation of heat. Unlike traditional heat pipes, however, the performance of thin heat pipes is heavily dependent on details of the internal heat pipe structure, including the vapor core geometry and structural mechanical characteristics. In this study, the development and testing of a new computational modeling and optimization tool are presented for the design of thin flat heat pipes. The computational model is described in detail and includes parameters that define properties of the liquid wick, vapor core, and structural case. The model is coupled to a gradient-based optimization procedure that minimizes a multi-objective cost function for a range of operating conditions. The cost function is expressed as the weighted sum of the total temperature drop, the liquid/vapor pressure ratio, the total mass of the heat pipe, and the structural deflection of the heat pipe during operation. The combined computational modeling and optimization tool is then used to design a copper-methanol flat heat pipe for a small satellite mission, where the optimization is performed with respect to both cold and hot orbital conditions. Validation of the optimized heat pipe is performed using computational fluid dynamics (CFD) simulations of the initial and final designs.