An approximate method for solving a class of non-linear optimal control problems with distributed parameters is presented. Approximate techniques, such as the Galerkin method, the Gauss principle and the integral method, are used to transform the original minimum time problem with distributed parameters into a corresponding problem with the lumped parameters. The lumped parameter system is analysed by the Pontryagin maximum principle. Using the Warner algorithm, numerical results are obtained for the minimum time problem of non-linear heat conduction. The influence of different physical parameters on the final results are analysed in detail.