Heating integrated in a transverse plane as a function of time for three different cases in which the change from sausage to kink takes place in 1, 0.7, or 0.4 periods, respectively, from left to right. The green curve is the actual heating, which depends on the phase of the wave. The blue curve is the envelope of this heating for all possible phases; it represents the maximum heating attainable. The red curve (right axis) shows the mean superoscillation factor. The highest heating rates coincide in time with the highest superoscillation.