A mathematical model for the synergistic interaction of physical and chemical environmental agents was suggested for quantitative prediction of irreversibly damaged cells after combined exposures. The model took into account the synergistic interaction of agents and was based on the supposition that additional effective damages responsible for the synergy are irreversible and originated from an interaction of ineffective sublesions. The experimental results regarding the irreversible component of radiation damage of diploid yeast cells simultaneous exposed to heat with ionizing radiation ($^{60}Co$) or UV light (254 nm) are presented. It was shown that the cell ability of the liquid holding recovery decreased with an increase in the temperature, at which the exposure was occurred. A good correspondence between experimental results and model prediction was demonstrated. The importance of the results obtained for the interpretation of the mechanism of synergistic interaction of various environmental factors is discussed.