An estimation method of the thermal conductivity of polymers during their crystallization is presented in this paper. The outputs of the established method depict the evolutionary profile of the thermal conductivity function of two coupled fields: the temperature and the relative crystallinity. The identification relies on the thermal response registered within the polymer during its solidification. A unidirectional heat transfer model is developed for this purpose and the thermal response of the polymer is coupled with the exothermal heat generation taking place during the crystallization. A hybrid optimization algorithm combining a stochastic method with a deterministic one is adopted for the resolution of the inverse heat conduction problem. The potential of the estimation algorithm in solving a complex and non-linear problem is validated in this study. The robustness of the inverse method is evaluated by taking into account the measurement noise as well as the uncertainties on apriori known thermal parameters. A sensitivity analysis is presented to assess the accuracy of the inverse problem outputs and emphasize the relationship between the identifiable parameters and the imposed cooling rate.