We study the thermodynamical and geometrical behaviour of the black holes t
hat arise as solutions of the heterotic string action. We discuss the near-
horizon scaling behaviour of the solutions that are described by two-dimens
ional Anti-de Sitter space (AdS(2)). We find that finite-energy excitations
of AdS(2) are suppressed only for scaling limits characterized by a dilato
n constant near the horizon, whereas this suppression does not occur when t
he dilaton is nan-constant. (C) 2000 Elsevier Science B.V. All rights reser
ved.