  We consider the thermodynamic properties of an exact black hole solution
obtained in Weyl geometric gravity theory, by considering the simplest
conformally invariant action, constructed from the square of the Weyl scalar,
and the strength of the Weyl vector only. The action is linearized in the Weyl
scalar by introducing an auxiliary scalar field, and thus it can be
reformulated as a scalar-vector-tensor theory in a Riemann space, in the
presence of a nonminimal coupling between the Ricci scalar and the scalar
field. In static spherical symmetry, this theory admits an exact black hole
solution, which generalizes the standard Schwarzschild-de Sitter solution
through the presence of two new terms in the metric, having a linear and a
quadratic dependence on the radial coordinate, respectively. The solution is
obtained by assuming that the Weyl vector has only a radial component. After
studying the locations of the event and cosmological horizons of the Weyl
geometric black hole, we investigate in detail the thermodynamical (quantum
properties) of this type of black holes, by considering the Hawking
temperature, the entropy, specific heat and the Helmholtz free energy functions
on both the event and the cosmological horizons. The Weyl geometric black holes
have thermodynamic properties that clearly differentiate them from similar
solutions of other modified gravity theories. The obtained results may lead to
the possibility of a better understanding of the properties of the black holes
in alternative gravity, and of the relevance of the thermodynamic aspects in
black hole physics.
