The Coulomb interaction of a charged test particle with an electron plasma whose unperturbed velocity distribution has different temperatures along and across a certain axis is kinetic-theoretically investigated. In the linear approximation, the binary correlation being neglected, the electric potential and energy loss of a charged test particle and the dielectric constant are derived. By introducing an angular-dependent temperature, the dispersion relation and damping constant of plasma oscillations are written by the same form as in the case of an isotropic temperature plasma.