Pinch‐point instability analysis is used to study the effects of finite temperature on the time‐asymptotic pulse shapes of electrostatic and electromagnetic two‐stream instabilities. Their absolute or convective instability nature is established over the entire regime from instability threshold at finite temperatures to the cold‐plasma hydrodynamic limit. The analysis is based upon nonrelativistic Vlasov theory dispersion relations for streams and plasmas with Maxwellian thermal distributions.