Linear polyethylene (Lupolen 6041 D) and a polyethylene fraction (PE 2000) were investigated by WAXS at temperatures 8 K < T < 293 K. From the position and integral widths of the reflections the lattice constants (and expansion coefficients) and lattice distortions are determined. Lattice distortions are of the strain type, induced by inherent stresses. They increase with decreasing temperature up to similar to 50 K and then to lower temperatures a decrease is observed. This is explained by the decrease of the thermal expansion coefficients. For PE 2000 for some reflections a minimum in the integral widths at T similar to 38 K occurs. The explanation of this effect is given by the occurence of a stress induced martensitic transformation (orthorhombic to monoclinic) of part of the material. The corresponding weak reflections are observed.