This paper deals with heat transfer due to a periodic annular jet from an annular channel in the displacer induced by its reciprocal motion. Heaters are concentric strips of nickel foil each temperature of which is kept constant using a CTA system. When the reciprocal frequency is low, heat transfer is higher near the top dead center of the displacer i.e. the clearance between displacer and the cylinder end is small. As the frequency becomes higher, heat transfer due to the jet from the annular channel becomes predominant in the impinging region and among the phases (from top dead center) from 30° to 210°. Heat transfer in such region and phases is proportional to frequency to the 0.75th power and pressure to the 0.75th power. Heat transfer is correlated in dimensionless forms not only for phase and area averaged values but also for the impinging region and for phases while the jet enhances heat transfer.