Measurements in boreholes and internal radar horizons confirm the existence of polythermal structures in polar and subpolar glaciers and ice sheets. The occurrence of an intraglacial phase boundary makes it necessary to consider two layers and transition conditions between cold and temperate ice. The governing field equations and constitutive relations for a two-layer model are stated with emphasis on boundary and transition conditions. A reduced plane flow model is introduced by using dimensionless variables and performing a scale analysis. According to the stated aim of this paper a parallel-sided slab model is suitable for rough analyses of borehole measurements. Its governing equations are deduced, and their analytical and numerical treatment is discussed. Sensitivity tests reveal a strong dependence of moisture content profiles on the numerical value of the water diffusivity coefficient and especially on strain heating. ¿ American Geophysical Union 1988