For this purpose an optical fiber tip of an optical fiber temperature sensor is equipped with a gallium arsenide crystal. Starting at a light wavelength of 850 nm GaAs becomes optically translucent. Since the spectral position of the band gap is temperature dependent, it shifts about 0.4 nm/K. The measurement device contains a light source and a device for the spectral detection of the band gap. With the changing of the band gap, (0.4 nm/K) an algorithm calculates the temperature (all 250 ms).