A method is developed for the quantitative prediction of thermally induced residual stresses in polymeric materials. During processing, when the polymeric material is cooling down from an elevated temperature, to room temperature, a strain becomes 'frozen-in' the material. Different cooling processes will cause different amounts of the strain to become frozen-in. The residual stresses are then just a material response to the frozen-in strains at a uniform room temperature, well after processing. A link between thermal history and frozen-in strains is found to be the 'residual' temperature field. The thermo-mechanical response of the material to the applied residual temperature field is identical to the response to frozen-in strains only. By knowing the residual temperature field, the residual stress problem can be considered as a thermal stress problem, which can be solved using various commercial numerical packages. The numerical algorithm for determining the residual temperature field is also presented. It accommodates various elements of the Finite Volume mesh topology as the Finite Volume method is used to carry out the thermomechanical analysis. The procedure includes tracking integration paths always orthogonal to the solidification front at any point and numerical integration of frozen-in temperature gradients along them. The application of the method is illustrated by predicting residual stresses in a polymeric plate subjected to controlled cooling conditions.