  We study static and radially symmetric black holes in the multi-fractional
theories of gravity with $q$-derivatives and with weighted derivatives,
frameworks where the spacetime dimension varies with the probed scale and
geometry is characterized by at least one fundamental length $\ell_*$. In the
$q$-derivatives scenario, one finds a tiny shift of the event horizon.
Schwarzschild black holes can present an additional ring singularity, not
present in general relativity, whose radius is proportional to $\ell_*$. In the
multi-fractional theory with weighted derivatives, there is no such
deformation, but non-trivial geometric features generate a
cosmological-constant term, leading to a de Sitter--Schwarzschild black hole.
For both scenarios, we compute the Hawking temperature and comment on the
resulting black hole thermodynamics. In the case with $q$-derivatives, black
holes can be hotter than usual and possess an additional ring singularity,
while in the case with weighted derivatives they have a de Sitter hair of
purely geometric origin, which may lead to a solution of the cosmological
constant problem similar to that in unimodular gravity. Finally, we compare our
findings with other Lorentz-violating models.
