  Taking advantage of the representation of dilatonic gravity with the
$R^2$-term under the form of low-derivative dilatonic gravity coupled to an
additional scalar, we construct a general renormalizable model motivated by
this theory. Exact black hole solutions are found for some special versions of
the model, and their thermodynamical properties are described in detail. In
particular, their horizons and temperatures are calculated. Finally, the
corresponding one-loop effective action is obtained in the conformal gauge, and
a number of its properties -including the construction of one-loop finite
models-are briefly described.
