Hawking temperature of expanding cosmological black holes

In the context of a debate on the correct expression of the Hawking temperature of a cosmological black hole, we show that the correct expression in terms of the Hawking-Hayward quasilocal energy $m_H$ of the hole is $T=(8\pi m_H(t){)}^{-1}$. This expression holds for comoving black holes and agrees with a recent proposal by Saida, Harada, and Maeda.