The performance of a Ground Water Heat Pump (GWHP) is often impaired by the thermal recycling between the injection and the extraction well(s), and hence this phenomenon should be evaluated in the design of open loop geothermal plants. The numerical flow and heat transport simulation of a GWHP requires an expensive characterization of the aquifer to obtain reliable input data, which is usually not affordable for small installations. To provide a simple, fast and inexpensive tool for preliminary and sensitivity analyses, an open-source numerical code was developed, which solves the hydraulic and thermal transport problem of a well doublet in the presence of a subsurface flow. The code, called TRS (Thermal Recycling Simulator), is based on a finite-difference approximation of the potential flow theory. The method was validated through the comparison with flow and heat transport simulations with FEFLOW. Subsequently, TRS was run with different values of the aquifer and plant parameters. The correlation observed between some characteristic non-dimensional quantities permitted an empirical correlation to be developed, that describes the time evolution of the extracted water temperature. An example is given for the use of the numerical code and the formula in the dimensioning of an open loop geothermal plant.