This paper studies the instabilities of the flow around a heated grooved circular cylinder with a diameter of D. The main objectives of this study are to investigate the effects of groove shape, the groove location, and the Reynolds number (Re) to find an optimum rate of heat transfer of flow regimes. The selected Re was set between 50 and 200. The groove shape and the groove location vary. Two groove shapes are employed, including square and triangular cross-sectional geometries. The groove is placed at three different angles of θ = 0°, 45°, and 90° on the leading surface of the circular cylinder relative to the front stagnation point. To perform statistical analysis, the Taguchi method is used with a house code program for all effective parameters. Accordingly, based on the number of parameters, the optimum level and percentage of contribution each parameter in heat transfer enhancement is identified. It is found that the most significant parameters on heat transfer are the angle and shape of the groove. The results show that the effect of Re is not very significant. The triangular groove shape at θ = 45° generates maximum heat transfer rate with more than 12% increment as compared with square groove shape at an identical location.