Abstract: Estimation of the thermal conductivity of a material is a typical inverse heat conduction problem (IHCP). The temperature-dependant thermal conductivity estimation method of genetic algorithms (GA) is presented. A physical practical constraint that the value of thermal conductivity of a typical thermal protection material should not decrease with the temperature increasing, and a engineering practical constraint that the predicted temperature should be greater than the measurement values when the temperature is high, are taken into account in the algorithms. Then, the constrained estimation algorithm of thermal conductivity is developed by two methods, i.e., the increments estimation method and the penalty function method. After applying these constrained estimation methods to a typical case, it is found that, these estimation methods are feasible and they can overcome the shortcoming of the original unconstrained estimation method that some unphysical oscillations may appear in the estimation result when the measurement noise is significant. The estimated results are of more engineering meanings in practical applications.