In this work the thermal properties of poly (L-lactide)/multi-wall carbon nanotube (PLLA/MWCNT) composites have been investigated. Thermal conductivity was determined after measuring specific heat capacity (C-p), thermal diffusivity (D) and bulk density (rho) of composites. Thermal conductivity rises up to 0.345 W/m K at 5 wt.% after reaching a minimum value of about 0.12 W/m K at 0.75 wt.%. In order to understand the heat-conduction process, experimentally obtained thermal conductivities were fitted to an existing theoretical model. The much lower thermal conductivity of composites compared with the value estimated from the intrinsic thermal conductivity of the nanotubes and their volume fraction could be explained in terms of the obtained large thermal resistance (R-k) of 1.8 +/- 0.3 x 10(-8) m(2) K/W at nanotube-matrix interface. The CNT dispersion in the composites was analyzed by atomic force microscopy (AFM) and transmission electron microscopy (TEM). Although the thermal resistance dramatically reduces the estimated bulk thermal conductivity of composites, the existence of an interconnected conductive nanotube network for thermal diffusion in PLLA/MWCNT composites demonstrates that the addition of carbon nanotubes represents an efficient strategy in order to successfully enhance the thermal conductivity of insulator polymers. (C) 2012 Elsevier Ltd. All rights reserved.