A temperature sensor is provided with a temperature-sensitive element on a surface of a monocrystalline substrate, wherein the temperature-sensitive element is made of a platinum thin-film resistor and is produced as an epitaxial layer. The monocrystalline substrate can be an electrically insulating material, preferably &agr;-Al2O3 or MgO. Alternatively, the substrate may be an electrically conducting material, such as silicon, with an electrically insulating epitaxial layer arranged between the substrate and the platinum thin-film resistor. The platinum thin-film resistor epitaxial layer is preferably deposited by physical vapor deposition (PVD), chemical vapor deposition (CVD), or molecular beam epitaxy (MBE).