While generally inducing minimal heating in many biomedical applications, electric fields may still induce significant temperature gradients, particularly for pulses of short duration and AC (sinusoidal) fields of high frequency, such as microwaves. This paper extends a recent analysis of temperature gradients across a biological cell and membrane for single pulses [(A. L. Garner, et al., J. Appl. Phys.113, 214701 (2013).] to multiple pulses or AC fields where the time between the two pulses, or the period for AC signals, is shorter than the thermal diffusion time. We calculate profiles of the induced temperature changes and gradients across a biological cell for AC wave of different frequencies and show that the location of the peak temperature and gradient shifts toward the center of the cell during subsequent half-waves. Higher frequency fields induce higher temperature gradients with the temperature gradient shifts toward the center of the cell for subsequent cycles.