The present study addresses the problem of ignition of a single sodium droplet, which is an important issue for the nuclear facilities safety. The study follows the approach of previous works and extends the results of those papers to the case of radiative heat loss. The contribution of the thermal radiation is taken into account based on the P-1 approximation for thermal radiation transfer. An extension of solutions of the existing model is obtained in the presence of radiative heat loss for ignition time and critical temperature by exploiting the sensitivity of the process to large chemical activation energy. Different qualitative effects of varying the dimensionless convective heat loss parameter with ignition time and critical temperature are presented in the graphs. The results show that the inclusion of additional heat sink mechanism, that is, radiative heat loss, causes significant delays in the ignition time and reduces the critical temperature with respect to results of previous studies.