The aim of this work is the investigation of the electronic properties of NiTi alloyed with Cu, during the transition from the high temperature austenitic phase to the low temperature martensitic phase. Hereby, we systematically varied the copper concentration from 0 at. % to 20 at. % in 5 at. % intervals. By using temperature-resolved transport experiments, such as electrical resistivity, Seebeck coefficient and Hall effect, insights into the electronic transport mechanisms are obtained. We show that especially the charge carrier density changes strongly at the investigated martensitic phase transitions. In addition, thermal properties such as thermal conductivity and specific heat capacity are measured in order to draw a complete picture of the thermal behavior. The influence of the copper concentration on the electronic properties of the martensitic phase transition is further analyzed with the help of models in order to draw conclusions about the entropy of the electron system and to establish a correlation with the phase transition temperature.