  We study the low frequency absorption cross section of spherically symmetric
nonextremal d-dimensional black holes. In the presence of alpha' corrections,
this quantity must have an explicit dependence on the Hawking temperature of
the form 1/T_H. This property of the low frequency absorption cross section is
shared by the D1-D5 system from type IIB superstring theory already at the
classical level, without alpha' corrections. We apply our formula to the
simplest example, the classical d-dimensional Reissner-Nordstrom solution,
checking that the obtained formula for the cross section has a smooth extremal
limit. We also apply it for a d-dimensional Tangherlini-like solution with
alpha'^3 corrections.
