A numerical simulation is performed to study the flow structures and heat transfer characteristics of a heated transversely oscillating cylinder in a cross flow. The variations of flow and thermal fields are classified into a class of moving boundary problems. The moving interfaces between the fluid and cylinder have been considered. An arbitrary Lagrangian-Eulerian kinematic description method is adopted to describe the flow and thermal fields. A penalty consistent finite element formulation is applied to solve the governing equations. The subsequent developments of the vortex shedding and heat transfer characteristics around the heated cylinder are presented in detail. The effects of Reynolds number, oscillating amplitude, oscillating speed on the flow structures and heat transfer characteristics are examined. The results show that the interaction between the oscillating cylinder and vortex shedding from the cylinder dominates the state of the wake. The flow and thermal fields may approach a periodic state in lock-in regime. The heat transfer of the cylinder in the lock-in regime is enhanced remarkably.