Abstract: As is well known to all, in the solution of transient temperature field problems a finite element discretizaton in the space dimension will be used. However, in the time dimension we usually use the finite differnce discretization. The paper is concerned with analysis and comparision of two different calculating schemes, Crank-Nicholson formulation and Galerkin process, in the time dimension. Special emphasis is given to the application condition of this two schemes with regard to the short-time accuracy. Some examples are given, it will be seen that a quite good agreement was obtained between the error analysis and the numerical results. In the solution of transient temperatue field problems with nonlinear boundary conditions a satisfactory accurate "isotangent"iterative method, which is more fast to converge after only few steps, as suggested. At last, Also discuss the selection of mesh and time step, and how to obtain a more accurate numerical solution with the least machine time.