The two-phase slug flow, or the Taylor flow, is used in a variety of applications, including efficient heat transfer in pulsating heat pipes (PHPs). The heat transfer efficiency is due to the presence of liquid thin film surrounding the bubble and separating it from the hot wall. The thin film facilitates much faster heat dissipation by evaporation as compared with single-phase cooling. The thinness of the liquid film also creates significant difficulty for numerical simulation of Taylor bubbles, and the lower is the bubble velocity, the thinner is the liquid film. We carried out a 3D simulation of the hydrodynamics and heat transfer during motion of Taylor bubbles of gas in a capillary tube with a diameter of 2 mm in the velocity range of 0.05–0.5 m/s, resolving the near-wall region in detail. The distributions of the friction coefficient and heat flux on the wall along the bubble motion were obtained. It was shown that complex cascade recirculation zones appeared near the bubble and led to significant change in both shear stresses and heat flux near the wall as compared with a single-phase flow.