An analysis of the plane rigid—plastic flow of a thin layer compressed by flat rigid dies coupled with the heat transfer in the die-layer system is considered. The numerical model of the thin layer compression includes non-homogeneous plastic dissipation rate, heat flux of the contact friction and thermal resistance of the die-layer interface boundary. The rigid—viscoplastic relation of the effective yield stress with accumulated plastic strain, effective strain rate and temperature is assumed for the layer. The effects of the contact friction, thermal resistance and the die velocity on the hot compression of the thin steel workpiece are investigated.