  The action for a class of three-dimensional dilaton-gravity theories, with an
electromagnetic Maxwell field and a cosmological constant, can be recast in a
Brans-Dicke-Maxwell type action, with its free $\omega$ parameter. For a
negative cosmological constant, these theories have static, electrically
charged, and spherically symmetric black hole solutions. Those theories with
well formulated asymptotics are studied through a Hamiltonian formalism, and
their thermodynamical properties are found. The theories studied are general
relativity, a dimensionally reduced cylindrical four-dimensional general
relativity theory, and a theory representing a class of theories, all with a
Maxwell term. The Hamiltonian formalism is setup in three dimensions through
foliations on the right region of the Carter-Penrose diagram, with the
bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the
right one. The metric functions on the hypersurfaces and the radial component
of the vector potential one-form are the canonical coordinates. The Hamiltonian
action is written, the Hamiltonian being a sum of constraints. One finds a new
action which yields an unconstrained theory with two pairs of canonical
coordinates ${M,P_M; Q,P_Q}$, where $M$ is the mass parameter, which needs
renormalization, $P_M$ its conjugate momenta, $Q$ is the charge parameter, and
$P_Q$ its conjugate momentum. The resulting Hamiltonian is a sum of boundary
terms only. A quantization of the theory is performed. The Schr\"odinger
evolution operator is constructed, the trace is taken, and the partition
function of the grand canonical ensemble is obtained, the chemical potential
being the electric potential. The charged black hole entropies differ, in
general, from the usual quarter of the horizon area due to the dilaton.
