The oscillatory rotational motion of the elephant pinna is considered a key mechanism in metabolic heat dissipation. Limited experimental investigations have revealed that the flapping of the elephant's pinna is responsible for surface heat transfer enhancement. The objective of the present experimental and computational work is to investigate the physics of the flow induced by the pinna's motion and its effects on the heat transfer. This was accomplished by designing, fabricating and testing two full-size laboratory models of elephant pinnae: one rigid and one flexible, both instrumented with small size thermocouples for time-dependent surface temperature measurements. A constant heat flux is applied to both sides of each model which is rotated about a fixed edge with a frequency of 2 rad/s in an infinite domain at ambient conditions. Of interest is the study of the impact of the flexural strength of the model's material on surface heat transfer. Additional computer simulations of the flow and thermal fields revealed a hooked-shape vortex tube around the free edges of the flapping pinna. This result is confirmed by the flow visualization with smoke particles. Both experimental and computational results exhibit local surface temperature profiles characterized by a transient unsteady periodic variation followed by a steady periodic phase. Flow visualization indicated significant interaction between the vortical structures shed off the edge and the flexible model's boundary layer. It has been found that the cooling of the flexible model is enhanced by 30%.