Using the steady-state heat flux method, the effective thermal conductivity lambda of a particle bed is measured at room temperature, varying the external load P on the bed in the range of 3-30 kPa. Grains of various forms (debris, pebble, cubo-octahedral) and balls of different materials (polypropylene, sodium chloride, ceramics, diamonds, metals) of which the thermal conductivity of the solid measures 0.2-1500 W/(m K) are used. From the experimental dependencies lambda(P) = lambda(0) + Delta lambda(P), values for effective thermal conductivity in the absence of contact heat conduction lambda(0) and contact conductivity Delta lambda(P) are found. The analysis allowed us (a) to refine further our earlier evaluation (in the first part of this study Abyzov et al. (2013)) of the adequacy of models which do not take account of contact thermal conductivity (the differential effective medium model and those of Gusarov et al., Raghavan-Martin, Chiew-Glandt/Gonzo, Kunii et al., Zehner-Schlunder) and (b) to assess the capabilities provided by a number of models of contact thermal conductivity (those of Dul'nev-Sigalova, Kaganer, Gusarov and others). A model with nominally flat rough contacts between particles in the bed is proposed, which describes the observed effects for contact thermal conductivity. (C) 2013 Elsevier Ltd. All rights reserved.