A conventional radiation thermometer encompasses an infrared radiation sensor and a heatable and/or coolable radiation incidence window. The method and radiation thermometer according to the invention use the established dependence of the sensor signal U of the infrared radiation sensor on the temperature Tw of the radiation incidence window W (or any other heatable or coolable optical element in the beam path) for verifying its proper functional operation. Applying the method according to the invention, the radiation incidence window (or perhaps another optical element in the beam path) is heated up or cooled by activating an associated electric heating or cooling device. The resulting change ΔUw in the sensor signal U is detected, preferably in continuous fashion, as a function of the window temperature Tw and analyzed or verified for any deviation from an acceptable value or permissible range.