Provided is a process for producing an elastic heat spreader film, the process comprising: (a) providing a layer of an aggregate or cluster of multiple graphene sheets; (b) impregnating an elastomer or rubber into the aggregate or cluster as a binder material or a matrix material to produce an impregnated aggregate or cluster, wherein the multiple graphene sheets are bonded by the binder material or dispersed in the matrix material and the elastomer or rubber is in an amount from 0.001% to 20% by weight based on the total heat spreader film weight; and (c) compressing the impregnated aggregate or cluster to produce the heat spreader film wherein the multiple graphene sheets are substantially aligned to be parallel to one another and wherein the elastic heat spreader film has a fully recoverable tensile elastic strain from 2% to 100% and an in-plane thermal conductivity from 200 W/mK to 1,750 W/mK.