  Following the initial work of Calcagni et al. on the black holes in
multi-fractional theories, we focus on the Schwarzschild black hole in
multi-fractional theory with q-derivatives. After presenting its Hawking and
Hayward temperatures in detail, we verify these results by appealing to the
well-known Hamilton-Jacobi and null geodesic methods of the tunnelling approach
to Hawking radiation. A special emphasis is placed on the difference between
the geometric and fractional frames.
