  We study the thermodynamical and geometrical behaviour of the black holes
that arise as solutions of the heterotic string action. We discuss the
near-horizon scaling behaviour of the solutions that are described by
two-dimensional Anti-de Sitter Space AdS(2). We find that finite-energy
excitations of AdS(2) are suppressed only for scaling limits characterised by a
dilaton which is constant near the horizon, whereas this suppression does not
occur when the dilaton is non constant.
