The problem of instabilities in colliding ionized hydrogen beams, which has been treated by Kahn and Parker in the special case of zero temperature, is solved for the nonzero temperature case by taking Maxwell distributions for the equilibrium density functions. At sufficiently high temperature it is found that the random thermal motion will prevent growing oscillations. The boundary between the stable and unstable regions is plotted as a function of energy and density parameters. Certain phenomena associated with solar particle streams are discussed in terms of these results.