For successful cold rolling operation at elevated operating conditions, the existence of desirable minimum film thickness at the roll-strip interface and awareness of its controlling by adjusting the process variables such as roll speed, reduction ratio, lubricant types, and roll cooling system etc. are essential. Moreover, the studies of the lubricant's starvation in the inlet zone and its influence on the film thickness at high roll speeds considering viscous shear heating effects are very important issues. Thus, the objectives of this paper are to analyze the inlet zone of cold rolling interface thermohydrodynamically and develop formulas for the prediction of minimum film thickness (for both isothermal and thermal cases) as functions of operating parameters including levels of starvation. Based on the investigations reported herein, it is observed that the existence of starvation up to certain level seems to be beneficial. It causes reduction in the temperature rise in the inlet zone and reduces the quantity of lubricating oil (leading to oil conservation) required during the cold rolling operation provided a thin continuous film exists at the strip-roll interface. Authors believe that the cold rolling industries may be benefited by the formulas reported in this paper.