Abstract The goal was to describe by a complex equation deformation resistance of a preheated Ti-IF steel in the wide temperature range. The mean flow stress was determined by an original procedure, based on laboratory rolling of flat samples and measurement of the rolling forces. The samples were austenitized at temperature 1120 °C and then air-cooled to the forming temperature. Separate models describing deformation resistance were developed for three temperature regions – ferrite, ferrite + austenite, or austenite. These models describe experimentally obtained data in the applied wide range of deformation conditions with a good accuracy. By their integration in the cumulative function a unique model was developed that reflect influence of temperature, strain, strain rate and phase composition on deformation resistance of the investigated IF steel. Particular members in this cumulative function are multiplied by coefficient 1 or 0, in dependence on a specific temperature. Calculation of specific coefficients had to be proposed in such a way so that they could react to surpassing of temperature boundaries between individual phase regions. The new cumulative function was compared with those obtained after direct heating of samples to the forming temperature. The integrated model can be used in off-line predictions of power/force parameters of forming of Ti-IF steel, in a wide range of conditions of hot and warm deformation. Achieved data confirmed theoretical assumptions about decrease in deformation resistance due to occurrence of the softer ferrite phase in low carbon steels. Relatively low deformation resistance of ferrite can be utilized favourably in ferritic rolling of IF steel.