A heat spreading material is integrated into a composite die structure including a first IC die having a first dielectric material and a first electrical interconnect structure, and a second IC die having a second dielectric material and a second electrical interconnect structure. The composite die structure may include a composite electrical interconnect structure comprising the first interconnect structure in direct contact with the second interconnect structure at a bond interface. The heat spreading material may be within at least a portion of a dielectric area through which the bond interface extends. The heat spreading material may be located within one or more dielectric materials surrounding the composite interconnect structure, and direct a flow of heat generated by one or more of the first and second IC dies.