In this study we investigated fluid displacement water with supercritical (sc) CO2 in chalk under conditions close to those used for geologic CO2 sequestration (GCS), to answer two main questions: How much volume is available for scCO2 injection? And what is the main mechanism of displacement over a range of temperatures? Characterization of immiscible scCO2 displacement, at the pore scale in the complex microstructure in chalk reservoirs, offers a pathway to better understand the macroscopic processes at the continuum scale. Fluid behavior was simulated by solving the Navier-Stokes equations, using finite-volume methods within a pore network. The pore network was extracted from a high resolution 3D image of chalk, obtained using X-ray nanotomography. Viscous fingering dominates scCO2 infiltration and pores remain only partially saturated. The unstable front, developed with high capillary number, causes filling of pores aligned with the flow direction, reaching a maximum of 70% scCO2 saturation. The saturation rate increases with temperature but the final saturation state is the same for all investigated temperatures. The higher the saturation rate, the higher the dynamic capillary pressure coefficient. A higher dynamic capillary pressure coefficient indicates that scCO2 needs more time to reach capillary equilibrium in the porous medium.