Temperature plays an important role in activating dislocation-obstacle interaction mechanisms such as cross slip, and the ability of dislocations to bypass obstacles like precipitates impacts the macroscale mechanical properties of engineering metals and alloys. In this work, we advance a combined 3D phase-field dislocation dynamics (PFDD) and kinetic Monte Carlo (kMC) mesoscale technique to simulate thermally activated cross slip of extended screw dislocations in face-centered cubic (FCC) metals. Reaction rates for obstacle shear and cross slip are calculated directly from athermal PFDD simulations and incorporated into the PFDD-kMC framework. Simulations across a range of temperatures and applied stresses show that the activation energy determines whether a dislocation shears or cross slips to bypass an obstacle. In both scenarios, the dislocation glides in a segmented manner, with a tortuosity that increases with both temperature and applied stress.