Heat sinks filled with phase-change material, a design concept suitable for the thermal management of electronic airborne systems, find limited applicability at present due to lack of structural rigidity and poor isothermal cooling characteristics. A composite heat sink device (CHSD) is a new design concept proposed in this work, which combines the thermal benefit of the phase-change material with the structural rigidity provided by a solid porous matrix. The device consists of a solid porous matrix with pores filled with capsules containing a phase-change material. Numerical simulations of a CHSD steady-model indicate the existence of a maximum capsule density beyond which a transition from disperse diffusion (when all capsules actively participate in the diffusion process) to concentrate diffusion (when the capsules close to the heated surface shield the capsules placed further away) occurs. This observation is important for optimizing the volume of the CHSD.