A treatment is given of the one‐dimensional problem of beam‐plasma interaction, including the effects of plasma and beam thermal velocities and momentum transfer collisions in the plasma. The conditions under which the Landau damping due to the plasma is negligible are first investigated. Neglecting this damping, a weak‐beam approximation to the dispersion relation is derived, and conditions for its validity are established. Expressions are derived for the maximum temporal and spatial growth rates in the limits of cold and hot beams, and few and many collisions. The growth rates given by the weak‐beam approximation are compared with those calculated from the full dispersion relation. The transition from a cold to a hot beam is discussed in terms of the topology of the roots of the dispersion relation, and also in terms of the location of the phase velocities of the most unstable waves relative to the bump in the distribution.