Abstract Limits in the application of a cold plasma model to whistler propagation in the magnetospheric plasma are studied. It is pointed out that finite anisotropy of magnetospheric plasma can compensate for the influence of finite temperature on whistler propagation so that the cold plasma model can be applied. An approximate formula is obtained for whistler refractive index for the case of oblique propagation in a hot anisotropic plasma with a loss cone. This formula is applied to the problem of whistler energy focusing along the magnetic field in the homogeneous plasma and whistler mode propagation in magnetospheric ducts. The possibility of whistler trapping in ducts formed by temperature gradients in the magnetospheric plasma is pointed out.