Abstract The thermal conductivity of plastics is relatively small and for this reason not easily measured. That is why the results in the literature vary sharply. Therefore measurements were made in the German Plastics Institute of the thermal conductivity of plastics with different methods and the results checked against each other. As the overall agreement is very good, we shall give the results only from a quasistationary method which works over a large temperature range. A good thermal contact at the surface of the sample is decisive. Therefore we had to abandon high vacuum as thermal insulation in favor of helium gas, which gives a good and exactly evaluated thermal contact. Thermal losses to the outside had to be prevented by guard rings. We deal first with amorphous high polymers. Their thermal conductivity varies only slightly with temperature even if one goes through the second-order transition region. However, a break in the curve of the thermal conductivity, is characteristic that is to say, a jump of the thermal coefficient at the second-order transition temperature. Figures 1–3 show this for natural rubber, Vulkollan (a crosslinked polyester-urethane elastomer), polyisobutylene, and polyvinyl chloride with different contents of plasticizer. The dependence on the concentration of plasticizer is the same for the break in the thermal-conductivity curve as for the second-order transition temperature. The systematic variation of the thermal conductivity with temperature which has been described seems to be valid in general for amorphous substances with molecules which have the form of a chain. For instance, even selenium, when displaced from the melt, Figure 4, passes smoothly through the second-order transition point without the extreme maxima and minima which have been seen by other authors and which are due to peculiarities in the experimental arrangement used.