Current-voltage (IV) characteristics have been studied in films of chemically-derived graphene (CDG) nano-flakes in lateral-diode geometry over temperature range from 300 to 5K. The CDG nano-flakes featured high polydispersivity with sizes varying from 20 to 300 nm as reveled by transmission electron microscopy. We found a positive temperaturedependent electrical conductivity over the whole temperature range and pronounced non-linearity in IV-characteristics at T<80K. The experimental data cannot be fitted using the Schottky-diode effect model or conventional thermally-activated behavior. In this work, we demonstrate that the obtained puzzling results can successfully be described within an Effective Medium approximation model we recently suggested for band-transport heterogeneous materials with spatial energy variation of the transport-band edge.