Hot stamping is a manufacturing process that can be used to produce complex-shaped parts with high mechanical properties. In this process, the part quality and the production rate are strongly influenced by the efficiency of the cooling system within the tool. Improving the efficiency of the cooling system is therefore a key factor in reducing production time and costs. Traditional cooling systems for hot stamping tools often rely on simple drilled channels, limiting their potential for optimization. But recent improvements in additive manufacturing of steel have made it possible to design and produce cooling channels of more complex shapes and therefore allow the use of innovative design approaches such as topology optimization. This paper proposes a new rational method for optimum design of cooling system for additively manufactured hot stamping tools. The proposed new methodology is based on fluid-thermal topology optimization (TO). A low-fidelity model using the Stokes-Darcy equations is used to simulate fluid flow in the cooling channels. The objective function and constraints are designed to minimize the maximum temperature of the tool surface (cooling efficiency) with limited pressure drop of the cooling system. Advanced computations techniques including parallel computation, stabilization techniques, adaptive mesh and iterative solvers are used to ensure the computation performance. The procedure developed is first tested on a simple example to check the consistency of the results obtained. Then, to demonstrate the contribution of our work to the field under study, the procedure developed is used to optimize the design of the cooling system for an industrial hot stamping punch to be additively manufactured. The obtained optimum design is compared with standard drilled channels design and the deign with shell and core technology (with insert). These comparisons clearly shows that the optimal design combined with additive manufacturing can reduce quenching time by 37% compared to conventional drilled straight channels, with very similar pressure drop and very similar load-bearing capacity. This research offers significant potential for improving efficiency and reducing costs in hot stamping and other manufacturing processes.