The present work deals with the measurement of thermo-physical properties of a freestanding sheet of graphene (thermal diffusivity and thermal conductivity), and their dependence on sample density as result of uniform mechanical compression. Thermal diffusivity of graphene nano-platelets (thin slabs) was measured by the pulse flash method. Obtained response data were processed with a specifically developed least square data processing algorithm. GNP specific heat was assumed from literature and thermal conductivity derived from thermal diffusivity, specific heat and density. Obtained results show a significant difference with respect to other porous media: the thermal diffusivity decreases as the density increases, while thermal conductivity increases for low and high densities, and remain fairly constant for the intermediate range. This can be explained by the very high thermal conductivity values reached by the nano-layers of graphene and the peculiar arrangement of platelets during the compression applied to the samples to get the desired density. Due to very high thermal conductivity of graphene layers, the obtained results show that thermal conductivity of conglomerates increases when there is an air reduction due to compression, and consequent density increases, with the number of contact points between platelets also increased. In the intermediate range (250 ≤ ρ ≤ 700 kg·m^-3) the folding of platelets reduces density, without increasing the contact points of platelets, so thermal conductivity can slightly decrease.