This paper investigates a new geometry of hybrid photovoltaic/thermal (PV/T) solar collector used as an evaporator in a CO2 transcritical heat pump system. The solar absorber plate embeds monocrystalline silicon PV cells producing electricity and a stainless steel sheet to improve heat transfer with respect to standard back sheets. A serpentine stainless steel tube is bonded to the back of this solar absorber plate and two-phase CO2 flows inside this heat exchanger. A semi-transient numerical model is proposed to assess the thermal and electrical performances of the evaporator under given weather parameters and heat pump operating conditions. The 2-D, transient thermal diffusion equation is combined with a 1-D, steady state, compressible, two-phase flow model to compute the temperature distribution of the solar absorber plate along with the pressure, velocity, density and enthalpy field of the CO2 in the serpentine tube. A special model based on the straight fin analytical model accounting for the circumferential temperature gradient around the tubes is developed to combine the absorber plate and the heat exchanger models. The simulation results show an overall mean temperature reduction of the solar absorber plate operating at an electrical maximum power point of more than 25 degrees C with respect to a standard PV collector. Reducing the plate temperature leads to an additional production of 34 W of electrical power exceeding the maximum power specified under the test conditions of IEC 60904-3 international standard. In the simulated conditions, 1.028 kW of thermal power is also extracted and can be used in heating applications. The electrical efficiency increases from 14.1% for a standard solar PV collector to 16.0% for the suggested evaporator design. Finally, an overall efficiency combining both the electricity and heat production of 72.3% is achieved.