The influence of the rapid solidification technique and heat treatment on the martensitic transformation, magnetic properties, thermo- and magnetic induced strain and electrical resistivity is investigated for the Cu doped NiMnGa Heusler-based ferromagnetic shape memory ribbons. The martensitic transformation temperatures are unexpectedly low (below 90 K—which can be attributed to the disordered texture as well as to the uncertainty in the elements substituted by the Cu), preceded by a premartensitic transformation (starting at around 190 K). A thermal treatment slightly increases the transformation as well as the Curie temperatures. Additionally, the thermal treatment promotes a higher magnetization value of the austenite phase and a lower one in the martensite. The shift of the martensitic transformation temperatures induced by the applied magnetic field, quantified from thermo-magnetic and thermo-magnetic induced strain measurements, is measured to have a positive value of about 1 K/T, and is then used to calculate the transformation entropy of the ribbons. The magnetostriction measurements suggest a rotational mechanism in low fields for the thermal treated samples and a saturation tendency at higher magnetic fields, except for the temperatures close to the phase transition temperatures (saturation is not reached at 5 T), where a linear volume magnetostriction cannot be ruled out. Resistivity and magnetoresistance properties have also been measured for all the samples.