According to the all set theory, a fuzzy-random heat conduction model is presented. To deal with the function, the following steps are taken. Firstly equations of the mean values and variances of the random thermal function are transformed. Secondly when the heat conduct parameters are the fuzzy numbers and the temperature boundary conditions are the random numbers, interval equations of the heat conduction are presented. Thirdly comparing the interval result in interval analysis with the one in confidence interval, the result in the interval analysis is larger than that in the confidence interval. Then the error expecting equation is presented. Finally, the interval analysis to deal with the stability heat conduction is given.