During the closing process of a vacuum interrupter, bounce arcs may be generated under high voltage, leading to the melting and welding of the contact surfaces. Recently, experimental research has been conducted in order to understand the bounce arc characteristics and reduce the contact welding. However, the mechanism research based on the modeling and simulation is rare. This paper is to study the development of bounce arc and the transient anode temperature under the erosion of the arc. A transient self-consistent model is established using the dynamic meshing technology. The influences of bouncing velocity and inrush current on the bounce arc expansion and the transient anode temperature are studied. The simulations predict that the bounce arc area increases with the decrease of bouncing velocity. The maximum temperature of the anode is higher with a slower bouncing velocity. Besides, the numerical results show that the spatial distribution of anode surface temperature changes with different inrush currents.