A new method of calculating the temperature of strongly radiative shocks (Mihalas number of order unity or lower) is proposed. By including ionization, radiative energy and radiative flux terms in the Rankine-Hugoniot jump conditions across the shock front, a new, self-consistent method of calculating the temperature of radiative shocks is developed. The method is compared to those used to calculate temperature in previous works using similar methods, including those which partially included radiative and/or ionization effects. The method is also compared to experimental data, taken from the literature, as well as SESAME equation of state tables and radiative hydrodynamics simulations. The results show the importance of including all radiative terms for the case of strongly radiative shocks. This result has important implications for the design and interpretation of future laboratory experiments where ever faster radiative shocks may be generated. Previously unseen phenomena could be accessible when the radiative energy plays a significant role in the system.