The effect of Reynolds number on a passive scalar field is investigated in the turbulent wake of a circular cylinder. The cylinder-diameter-based Reynolds number varies between 1200 and 8600. The temperature difference above the ambient temperature acts as a passive scalar quantity. In general, the Reynolds number is found to have significant influence on the scalar mixing characteristics in the wake flow. When Reynolds number increases, the mean scalar spreads out more rapidly and the scalar variance decays with downstream distance at a higher rate. It is also revealed that if is likely to have two regions where some relations for self-similarity are approximately valid, one is located in the late Karman vortex street and the other is the traditional self-preserving far-wake.