The need to address the global challenge of using clean energy, mitigating climatic changes and favoring sustainable development, has promoted the diffusion of new technologies for the use of renewable energy resources. Geothermal technologies can generate electricity and/or heating and cooling while producing very low levels Green House Gas (GHG) emissions and therefore play an important role in realizing these targets. In particular, low temperature applications have known a great development over the last years, thanks to the larger availability, compared to high temperature traditional ones, and to the increasing cooling demand that is also related to the global warming. A sustainable and profitable use of low enthalpy geothermal resources is strictly related to a correct analysis of ground thermal response to energy extraction/injection: in fact, sizing methodologies and optimization strategies are based on a balance of plant׳s energy demand and predictions of ground thermal variations due to these energy requirements. Therefore, an accurate mathematical modeling of thermo-dynamic behavior of the ground is fundamental for optimal design of geothermal plants for two reasons: it is the basis for the estimation of ground thermo-physical properties from the analysis of the Thermal Response Test, and it is essential in order to predict hour by hour (or short term) responses of the ground to continuously changing energy loads and therefore to estimate system energy consumption. Besides, there is a great interest in modeling thermo-fluid dynamic phenomena which occur in geothermal wells and geothermal heat exchangers as these can significantly affect the performance of the whole system.