A dual-phase structure consisting of the NaZn13-type (1: 13) matrix and a secondary (Fe, Co)-Si phase is designed in Fe-rich La-(Fe, Co)-Si compounds. As the extra-Fe doping altered Co content of the 1: 13 phase, the magnetic entropy change keeps to be a relatively large magnitude of 6.7-7.7 J/kgK in 265-290K for 2 T field change. In addition, mechanical properties were apparently improved by second-phase strengthening. The primary significance in this work is that the composition modification in matrix phase brings about a drastic increase in the thermal conductivity, which can be ascribed to the weakening effect of phonon point-defect-scattering. On the basis of Neilsen two-phase system model, the electrical conductivity of dispersed (Fe, Co)-Si phase plays very limited contribution to the enhanced thermal transport properties in composites. Our results demonstrate that the combined merits of high thermal conductivity, improved mechanical properties, large magnetic entropy change, and tunable transition temperature can be simultaneously realized in Fe-rich La-(Fe, Co)-Si composite materials. (C) 2015 AIP Publishing LLC