Use of oscillatory flow and phase-change material (PCM) microcapsules to enhance heat transport efficiency in micro/minichannels is among many new concepts and methodologies that have been proposed. In this paper, we propose a novel and simple heat spreader design concept that integrates the technologies of oscillating flow streaming and PCM microcapsules. Phenomenon of the flow streaming can be found in oscillating, zero-mean-velocity flows in many channel configurations. The pumpless bidirectional streaming flow can be generated by heating instability oscillation or by displacement of a lead zirconate titanate diaphragm. Discrepancy in velocity profiles between the forward and backward flows causes fluid and PCM microcapsules, suspended in the fluid near the walls, to drift toward one end while particles near the centerline move toward the other end. Flow streaming is a common mechanism in many biological systems but an innovative feature for heat transfer devices. We conducted preliminary work on scale analysis and computer simulations of suspended PCM microcapsules streaming in mini/microbifurcation networks. Computer simulated microcapsules distribution patterns are verified by visualization experiments reported in the literature. This work demonstrates that flow streaming with PCM microcapsule entrainment has the potential to be used as a cost-effective technology for a heat spreader design.