Improvements in using geothermal sources can be attained through the installation of power plants taking advantage of low and medium enthalpy available in poorly exploited geothermal sites. Geothermal fluids at medium and low temperature could be considered to feed binary cycle power plants using organic fluids for electricity “production” or in cogeneration configuration. The improvement in the use of geothermal aquifers at low-medium enthalpy in small deep sites favours the reduction of drilling well costs, and in addition, it allows the exploitation of local resources in the energy districts. The heat exchanger evaporator enables the thermal heat exchange between the working fluid (which is commonly an organic fluid for an Organic Rankine Cycle) and the geothermal fluid (supplied by the aquifer). Thus, it has to be realised taking into account the thermodynamic proprieties and chemical composition of the geothermal field. The geothermal fluid is typically very aggressive, and it leads to the corrosion of steel traditionally used in the heat exchangers. This paper analyses the possibility of using plastic material in the constructions of the evaporator installed in an Organic Rankine Cycle plant in order to overcome the problems of corrosion and the increase of heat exchanger thermal resistance due to the fouling effect. A comparison among heat exchangers made of commonly used materials, such as carbon, steel, and titanium, with alternative polymeric materials has been carried out. This analysis has been built in a mathematical approach using the correlation referred to in the literature about heat transfer in single-phase and two-phase fluids in a tube and/or in the shell side. The outcomes provide the heat transfer area for the shell and tube heat exchanger with a fixed thermal power size. The results have demonstrated that the plastic evaporator shows an increase of 47.0% of the heat transfer area but an economic installation cost saving of 48.0% over the titanium evaporator.