The lattice thermal conductivity of compact random silicon and germanium nanowire composites was investigated by using a Monte-Carlo (MC) simulator, which was developed based on the gray medium approximation and unstructured grids. By defining the local equilibrium temperature as the one which preserves the local phonon energy in the interested heterogeneous subregion, we are able to obtain the effective thermal conductivity of random nanowire composites and explore the effects of the wire shape and the composition concentration on it. The results show that among the three kinds of wire shapes investigated - triangle, quadrangle, and voronoi, the random quadrilateral nanowire composites are the best thermal conductor under a fixed interface density or a fixed characteristic wire size and that the dependence of the effective thermal conductivity on the silicon volume concentration is approximately parabolic. The influences of these two factors are equally strong. Moreover, the parabolic dependence can be well explained by the effective medium approximation model for three bond percolation systems. (C) 2012 Elsevier Ltd. All rights reserved.