  The thermal evolution of the intergalactic medium (IGM) can serve as a
sensitive probe of cosmological heat sources and sinks. We employ it to limit
interactions between dark matter and baryons. After reionization the IGM
temperature is set by the balance between photoheating and adiabatic cooling.
We use measurements of the IGM temperature from Lyman-$\alpha$-forest data to
constrain the cross-section $\sigma$ between dark matter and baryons, finding
$\sigma < 10^{-20}$ cm$^2$ for dark-matter masses $m_\chi\leq 1$ GeV. This
provides the first direct constraint on scattering between dark matter and
baryons at redshift $z\sim5$.
