In nuclear physics experiments, a typical engineering issue is the dissipation of heat from very small surfaces and volumes on which a significant amount of energy is thermally deposited by a small-sized beam of particles. This article describes a finite element method simulation methodology for heat dissipation and the subsequent design and development of the holder of a lithium-based target up to its construction. The target described in the paper is used to study the 7Li(p,e+e-)8Be process with the proton Cockcroft–Walton accelerator of the MEG experiment at the Paul Scherrer Institut (Villigen, Switzerland). The material of the target region crossed by the emitted e+e- has to be reduced as much as possible to minimally perturb the measurement of their momenta, and a thin target is required. In order to ensure the dissipation of the thermal load on the target, an in-depth thermomechanical and structural simulation was realized using ANSYS. This allowed to verify the efficiency of the dissipation mechanisms, the maximum temperatures reached, and the thermal stress on all parts to ensure a sufficiently long lifetime of the target for the physics process measurement. To realize an optimized geometry ensuring continuity of the thermal flux—essential to dissipate the incoming power—the additive manufacturing was deemed necessary. The target support has been realized in pure copper, exploiting its excellent conductive properties and the cutting-edge additive manufacturing technologies, recently developed to overcome the inherent difficulties of Laser Powder Bed Fusion (L-PBF) technology to this material.