Computationally intensive problems are often encountered in numerical heat transfer studies. One of the major cause is the small time steps brought forth by the fine spatial grid required at critical regions. Consequently, computational efficiency becomes one of the key issue in such numerical studies. By and large, the existing methods for enhancing computational efficiency either are only applicable for iterative operations, or provide limited speed-up because the solutions at the certain regions within the domain are marching with an unnecessary small time step. This work presents the development of a new method which achieves a higher computational efficiency. This method is herein referred to as the Multi-Spatial-Temporal Grid (MSTG) method, and it provides a significant speed-up by simultaneously implementing grid reduction and multiple timesteps. This method has been tested to be effective in improving the computational efficiency of conduction problem in transient multi-dimensional orthogonal coordinates. Current benchmarking showed the solution obtained from this method to be within 0.04% of those obtained from a uniform grid. In addition, the speed-up of this scheme was found to be significantly higher than most existing methods.