The principal challenge in developing a new thermal interface material (TIM) is to co-design its micro-attributes (e.g. filler type, packing fraction, size distribution) that simultaneously ensure high effective thermal conductivity (Keff), low elastic modulus (Eeff) and low viscosity (neff). Today there exists little physical insight into size distributions of fillers that would optimize desired properties. These thermo-mechanical metrics follow contradicting trends if filler content is only monotonically increased. In this paper, we elucidate micro structure -property correlations vital for optimizing effective properties. First, we systematically vary filler size distributions and generate different particulate structures with a previously developed packing algorithm . Then, we employ mechanistic models, based upon physics of micro-scale heat/force transport, to predict Keff Eeff and neff of the particulate structure, thereby identifying filler size domains that optimize the desired properties.