In this diploma work we will be dealing with conduction heat transfer in the context of geothermics, In first chapters, the basics of the physics of heat transfer will be reviewed. We will also discuss basics of geothermics with some remarks on application of geothermal energy to economical issues. The basics of downhole heat pumps will be shown. In the remaning chapters we will be focusing on cunduction heat transfer and develop basic theory of the heat equation. With the solutions of the heat equation we will loook at the impact radius of downhole heat pump on the surrounding temerature field.