In this paper, an unbounded, collision‐free magnetoplasma of one species is analyzed by applying linearized theory. Modifications on the cold plasma dispersion surfaces due to the temperature effect are indicated by typical examples. To take into account the particle‐wave interactions, a microscopic model of the magnetoplasma is analyzed for very large refractive indices and for very high temperatures. Two directions of propagation (along and across the biasing magnetic field B_º) are considered, According to the results of the microscopic model, at gyroresonance for propagation along B_º the complex refractive index n cannot have arbitrarily large values if its phase angle is between −π/4, and π/4, whereas, for propagation across B_º, η becomes real and arbitrarily large. Both of these results contradict those of the compressible fluid model.