  We study the absorption of a minimally coupled scalar in the gravitational
background created by a stack of near-extremal black three-branes, and more
generally by M2, M5 and Dp branes. The absorption probability has the form P(l)
= P_0(l) f_l(\lambda), where P_0(l) is the partial wave's absorption
probability in the extremal case, and the thermal factor f_l(\lambda) depends
on the ratio of the frequency of the incoming wave and the Hawking temperature,
\lambda = \omega/\pi T. Using Langer-Olver's method, we obtain a
low-temperature (\lambda \gg 1) asymptotic expansion for P(l) with coefficients
determined recursively. This expansion, which turns out to be a fairly good
approximation even for \lambda \sim 1, accounts for all power-like
finite-temperature corrections to P_0(l), and we calculate a few terms
explicitly. We also show that at low temperature the absorption probability
contains exponentially suppressed terms, and attempt to develop an
approximation scheme to calculate those. The high-temperature expansion is also
considered. For the s-wave, the low-temperature gravity result is consistent
with the free finite-temperature field theory calculation, while for high
temperature and higher partial waves we find a disagreement. As a check of the
approximation methods used, we apply them to the D1-D5-brane system, and
compare results to the known exact solution.
