The thermal conductivity of five semi-crystalline and four amorphous polymers was determined within a wide range of temperature, starting at room temperature and going up to temperatures above the polymer melting point (Tm) for semi-crystalline polymers or above the glass transition temperature (Tg) for amorphous polymers. Two transient techniques were employed in the experimental investigation: the hot wire technique for the group of amorphous polymers, and the laser flash technique for the semicrystalline polymers. As expected, the experimental results show that Tg exerts a measureable influence on the thermal conductivity of amorphous polymers. In the case of semi-crystalline polymers, a singular behaviour of the thermal conductivity is observed within the Tm range. In order to explain the anomalous behaviour, the influence of these transition temperatures on the thermal conductivity behaviour with temperature has been analysed in terms of a phonon conduction process and temperature variations of specific heat and modulus of elasticity of the analyzed polymers.