The influence of liquid critical clusters temperature fluctuations caused by the radiation exchange (RTFs) on the nucleation process during a vapor to liquid phase transition is studied. This influence is significant when two conditions are met; (1) the RTFs amplitude is larger than the system overcooling thus allowing a reduction in the cluster temperature below the temperature of phase transition, and (2) RTFs correlation time is large enough to allow an extra emission of vapor molecules by the cluster of critical size thus making the cluster subcritical. The range of the system overcooling is found where RTFs may have a strong impact on the process of liquid phase formation.