In this paper the open, circular cross-section cylindrical gyro- electric p-GaAs (semiconductor-dielectric) waveguides with temperature-sensitive anisotropic dielectric layer are investigated. The gyroelectric phase shifters without anisotropic dielectric layer are not effective. The anisotropic layer increases the mode HE₁₁ differential phase shift to 1060° and 1250°, when temperature T = (125–200) K, N = 5∙10¹⁹ and N = 10²⁰ m^–3 respectively. Propagated mode HE₁₁ in gyroelectric p-GaAs waveguides, the attenuation coefficient increases, increasing the concentration of holes. The anisotropic dielectric layer reduces the mode attenuation, it is appropriate to create gyroelectric mode phase shifters with a lower hole concentration and anisotropic dielectric layer.