A cold plasma approximation is often employed when deriving a wave dispersion relation for a beam-plasma system in which the beam width is considered to be a factor in the wave dispersion. This approximation may no longer be valid for a sufficiently thin beam whose width is comparable to the Larmor radius, and temperature should be included in the model. As an initial attempt to take into account warm plasma effects we treat temperature as a first-order correction to the cold dispersion relation. Temperature dependent wave fields are found for solutions of the cold model dispersion relation, and we choose to present solutions for frequencies above the electron gyrofrequency when the electron gyrofrequency is greater than the electron plasma frequency. Since temperature enters as a correction term, some knowledge of the wave field eigenfunctions is required, and one example of both the cold model fields and the temperature corrections to these fields is given. Determining the form of the wave eigenfunctions is also a useful indicator of how electrostatic the waves are, which is of some importance in simplifying a finite geometry warm plasma dispersion relation. By comparing the correction fields to the cold model fields it is possible to determine a critical thermal velocity for which the temperature corrections become significant. A temperature of 0.25 eV for a 2.5-keV electron beam is shown to be a reasonable limit for the validity of a cold plasma approximation. Since the temperature is not just a beam temperature but also a background plasma temperature, this result may have implications for both magnetospheric and laboratory electron beam instabilities.