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Abstract Hawking temperature has been widely utilized in the literature as the temperature that corresponds to various nonextensive entropies. In this study, we analyze the compatibility of the Hawking temperature with the nonextensive entropies. We demonstrate that, for every nonextensive entropy, one may define an effective temperature (which we call equilibrium temperature) by utilizing the equilibrium condition, and that there is always an additive equilibrium entropy associated with this effective temperature. Except for Bekenstein entropy, we show that Hawking temperature is thermodynamically inconsistent with other nonextensive entropies. We focus on the equilibrium requirement for the Tsallis–Cirto black hole entropy and demonstrate that the Bekenstein–Hawking entropy is the related equilibrium entropy, and the Hawking temperature is the associated equilibrium temperature for the Tsallis–Cirto black hole entropy.