After DC and AC conductivity measurements, percolation parameters, universality, and time‐temperature‐concentration superposition are evaluated in biocomposites based on poly(lactide) loaded with multiwalled carbon nanotubes either carboxylic, PLA/c‐CNT, or pure but with a larger aspect ratio, PLA/LAR‐CNT, in weight concentrations up to 7%. The polymer matrix is either 100% amorphous or cold‐crystallized. Wide angle X‐ray scattering is used to extract the crystallinity at each temperature. The nucleating effect for the cold crystallization of the PLA is greater for the LAR‐CNT than for the carboxylic ones. DC and AC conductivities are measured in broad frequency and temperature ranges, from 1 mHz to 1 MHz and from 133 to 378 K, respectively. The critical percolation value increases for c‐CNTs (from 1.8 to 2.4 vol%) upon cold crystallization of the PLA matrix as the formation of a conductive path is hindered by the existence of a crystalline phase, which is dominant over the reduction of the amorphous regions. No significant changes upon crystallization were found in the critical concentration value (0.6 vol%) for the LAR composites, where the conductive path is 2D. The universal scaling found here for different concentrations is lost when temperature varies. However, time‐temperature superposition is present for each concentration of LAR or carboxylic CNTs. POLYM. COMPOS., 2013. © 2012 Society of Plastics Engineers