The analyses of large-scale numerical problems of mining domain such as heat dissipation from rock strata to the ventilation air in large network of underground mine galleries are usually time taking process and require huge computational resources. To overcome this issue, High Performance Computing system (HPC) can be utilized to expedite the numerical analysis process for solving the problems within a reasonable time. In order to utilize HPC, this paper developed parallel finite element codes for solving heat conduction problems of mine galleries. The developed C++ codes of parallel FE are applied in solving 1D and 2D heat conduction problems. For the comparative analysis of 1D and 2D problems, the number of unknown nodes is fixed. It is observed that the computational time reduced when the number of processors increased. On the other hand, the computational time took longer time in 2D problem in comparison to that in 1D. Graphics User Interface (GUI) is also developed in terms of number of nodes of mesh, the boundary temperatures and length of the element. To sum up, the work of this paper reveals that the parallel computing is highly efficient in solving the large scale numerical geo-mining problems.