Thin layers are widely used in electronics and protective coatings. They are also increasingly used in wearable electronics. A major challenge affecting the use of thin layers is their connection to flexible substrates, particularly textile products. This article describes the stability of the resistance of a silver layer with a thickness of 250 nm in a wide temperature range of 15–295 K. The aim was to determine the temperature dependence of the resistance of layers formed on a composite textile substrate compared with that of layers produced on an Al2O3 substrate. The results showed that the electrical parameters of the layer formed on the composite textile substrate changed in a manner atypical for metallic layers. This may have been due to the polyurethane base layer. The roughness and ability to deform under the influence of heat of the substrate can significantly affect the electrical parameters of a thin metal layer produced by the PVD coating process, which is important for the design of textronic applications.