  The intergalactic medium (IGM) prior to the epoch of reionization consists
mostly of neutral hydrogen gas. Ly-alpha photons produced by early stars
resonantly scatter off hydrogen atoms, causing energy exchange between the
radiation field and the gas. This interaction results in moderate heating of
the gas due to the recoil of the atoms upon scattering, which is of great
interest for future studies of the pre-reionization IGM in the HI 21 cm line.
We investigate the effect of this Ly-alpha heating in the IGM with linear
density, temperature, and velocity perturbations. Perturbations smaller than
the diffusion length of photons could be damped due to heat conduction by
Ly-alpha photons. The scale at which damping occurs and the strength of this
effect depend on various properties of the gas, the flux of Ly-alpha photons
and the way in which photon frequencies are redistributed upon scattering. To
find the relevant length scale and the extent to which Ly-alpha heating affects
perturbations, we calculate the gas heating rates by numerically solving
linearized Boltzmann equations in which scattering is treated by the
Fokker-Planck approximation. We find that (1) perturbations add a small
correction to the gas heating rate, and (2) the damping of temperature
perturbations occurs at scales with comoving wavenumber k>10^4 Mpc^{-1}, which
are much smaller than the Jeans scale and thus unlikely to substantially affect
the observed 21 cm signal.
