We present the results of calculations of the thermal conductivity and viscosity coefficients for a two-component fully ionized classical Coulomb plasma having ion charges from one to three, performed by the molecular dynamics method. The model of ultracold plasma was used, where particles interact according to the Coulomb law without any restrictions at large or small distances. The calculations are carried out in a wide range of the strong coupling parameter. Similarity for the coefficients of thermal conductivity and viscosity at multiple ionization is demonstrated. Comparison with the results of calculations for other plasma models is given. The results obtained can be used for any classical non-degenerate strongly coupled plasma.