  The development of cryogenic semiconductor electronics and superconducting
quantum computing requires composite materials that can provide both thermal
conduction and thermal insulation. We demonstrated that at cryogenic
temperatures, the thermal conductivity of graphene composites can be both
higher and lower than that of the reference pristine epoxy, depending on the
graphene filler loading and temperature. There exists a well-defined cross-over
temperature - above it, the thermal conductivity of composites increases with
the addition of graphene; below it, the thermal conductivity decreases with the
addition of graphene. The counter-intuitive trend was explained by the
specificity of heat conduction at low temperatures: graphene fillers can serve
as, both, the scattering centers for phonons in the matrix material and as the
conduits of heat. We offer a physical model that explains the experimental
trends by the increasing effect of the thermal boundary resistance at cryogenic
temperatures and the anomalous thermal percolation threshold, which becomes
temperature dependent. The obtained results suggest the possibility of using
graphene composites for, both, removing the heat and thermally insulating
components at cryogenic temperatures - a capability important for quantum
computing and cryogenically cooled conventional electronics.
