  We study the possible existence of black holes in scalar-tensor theories of
gravity in four dimensions. Their existence is verified for anomalous versions
of these theories, with a negative kinetic term in the Lagrangian. The Hawking
temperature T_H of these holes is zero, while the horizon area is (in most
cases) infinite. It is shown that an infinite value of T_H can occur only at a
curvature singularity rather than a horizon. As a special case, the Brans-Dicke
theory is studied in more detail, and two kinds of infinite-area black holes
are revealed, with finite and infinite proper time needed for an infalling
particle to reach the horizon.
