A new solution to the radial transient heat conduction has been developed for analyzing a thermal conductivity probe (TCP). The new analytical solution can better approximate the temperature responses than those from the classical solution of Carslaw and Jaeger (1959) when numerical results are compared with. Firstly, this paper theoretically analyzes the potential errors of the temperature responses of the TCP due to a number of parameters, such as, probe size, diameter ratio, heating power, thermal properties of TCP's materials and sampling media, and thermocouple location. With the new solution, the errors of temperature responses can be significantly reduced, which can be 100 times lower. Secondly, this paper also theoretically analyzes the evaluation errors of the thermal conductivity of a sampling medium (km) due to the new and classical solutions. The effects of the abovementioned parameters plus an initiating time (to) on evaluating km are studied in order to establish some design guidelines for the TCP. (C) 2015 Elsevier Ltd. All rights reserved.