In a method of making a thermal interface material, functionalized graphene sheets are dispersed in a liquid. The liquid is removed through a filter so as to form a filtration cake of aligned functionalized graphene sheets, substantially all of which are parallel to a common plane. At least one block of aligned functionalized graphene sheets is cut from the filtration cake. The block includes a first end face and an oppositely-disposed second end face that are parallel to each other and to which substantially all of the functionalized graphene sheets are transverse. The block also includes two oppositely-disposed sides to which substantially all of the functionalized graphene sheets are parallel. A first layer of a thermally conductive substance is applied to the first end face and a second layer of the thermally conductive substance is applied to the second end face of the block.