In this paper, the propagation of an oblique E-mode electromagnetic wave in a plane stratified collision-free plasma is investigated. A singularity associated with the electric field near the plasma resonance is shown to disappear when the effect of the finite temperature of the plasma is taken into account. By allowing for a weak spatial dispersion, a fourth-order warm-plasma field equation is obtained, and a connection formula based on an analytical continuation of integral solutions is deduced. The connection formula is then applied to the problem of mode coupling between electromagnetic E waves and electrostatic plasma waves.