A modified Chapman–Enskog analysis is employed to solve the relativistic Boltzmann transport equation. This is in the context of binary Coulomb encounter in a weakly coupled and fully ionized nondegenerate electron–ion plasma across a magnetic field. Specific formulas concerning transport coefficients are derived analytically in the various limits of temperatures, viz., nonrelativistic, moderately relativistic, and ultrarelativistic temperatures. Early classical results are equally recovered. The dependence of coefficients on thermal regimes is quantitatively discussed and their markedly diminishing trends are analyzed.