An analytical study of transient heat conduction with a moving heat source/sink is considered. In this study a closed form solution is obtained. By using the solution obtained, the spatial temperature distribution and the temperature-time history could be obtained. The results obtained are compared with the numerical and experimental data presented in Part II of this work. The comparison shows that the present solution can be used to determine the effect of different heat flow parameters on the temperature pattern and history in any similar heat conduction problems.