A note on the Vaidya-Hayward black hole

In view of a defect in the temperature of the Vaidya black hole, we consider a Vaidya-type generalization of the Hayward black hole. Its temperature and radius are obtained by an easy method. The rate of change of the horizon, i.e., $\dot {r}_{H}$ , is automatically restricted by the black hole itself. Based on the Stefan-Boltzmann law, the maximum value of $|\dot {r}_{H}|$ depends on a parameter characterizing quantum gravity effects, and is of the order of $10^{-6}$ . When the black hole's mass decreases to the minimum value, the horizon will cease to shrink and the temperature will vanish naturally.