Arrangement comprising: a laser beam source for producing a laser beam having a laser wavelength λ L in the infrared wavelength range, preferably of more than 2 μm, especially at λ L = 10.6 μm, and preferably at a power density of 1 kW/cm 2 or above, an optical element (9, 20) which is arranged in the beam path of the laser beam and which is transmissive or partially transmissive to radiation at a laser wavelength λ L in the infrared range, as well as an apparatus (26, 40, 50) for monitoring the temperature and/or a temperature-dependent parameter, especially the refractive index or the thermal conductivity, of the optical element (9, 20), the apparatus (26, 40, 50) comprising: - at least one measuring light source (28, 34; 41; 51) for producing measuring radiation and sending it onto the optical element (9, 20), - at least one detector (31, 36; 43; 56, 57) for detecting at least a portion of the measuring radiation that has passed through the optical element (9, 20), as well as - an evaluating device (33; 44; 58) which is connected to the detector (31, 36; 43; 56, 57) and which monitors the temperature and/or temperature-dependent parameter, which is correlated with the intensity of the detected measuring radiation, in a passage region (32, 37) of the measuring radiation based on a predefined relation between the intensity of the detected measuring radiation and the temperature and/or the temperature-dependent parameter in the passage region (32, 37), which relation is based on the temperature-dependent absorption of the transmissive or partially transmissive optical element (9, 20) in the passage region (32, 37), wherein the at least one measuring light source (28, 34; 41; 51) is configured to produce measuring radiation at a measuring wavelength λ M or in a measuring wavelength range of λ M ± Δλ that is different from the laser wavelength λ L. a laser beam source for producing a laser beam having a laser wavelength λ L in the infrared wavelength range, preferably of more than 2 μm, especially at λ L = 10.6 μm, and preferably at a power density of 1 kW/cm 2 or above, an optical element (9, 20) which is arranged in the beam path of the laser beam and which is transmissive or partially transmissive to radiation at a laser wavelength λ L in the infrared range, as well as an apparatus (26, 40, 50) for monitoring the temperature and/or a temperature-dependent parameter, especially the refractive index or the thermal conductivity, of the optical element (9, 20), the apparatus (26, 40, 50) comprising: - at least one measuring light source (28, 34; 41; 51) for producing measuring radiation and sending it onto the optical element (9, 20), - at least one detector (31, 36; 43; 56, 57) for detecting at least a portion of the measuring radiation that has passed through the optical element (9, 20), as well as - an evaluating device (33; 44; 58) which is connected to the detector (31, 36; 43; 56, 57) and which monitors the temperature and/or temperature-dependent parameter, which is correlated with the intensity of the detected measuring radiation, in a passage region (32, 37) of the measuring radiation based on a predefined relation between the intensity of the detected measuring radiation and the temperature and/or the temperature-dependent parameter in the passage region (32, 37), which relation is based on the temperature-dependent absorption of the transmissive or partially transmissive optical element (9, 20) in the passage region (32, 37), wherein the at least one measuring light source (28, 34; 41; 51) is configured to produce measuring radiation at a measuring wavelength λ M or in a measuring wavelength range of λ M ± Δλ that is different from the laser wavelength λ L. - at least one measuring light source (28, 34; 41; 51) for producing measuring radiation and sending it onto the optical element (9, 20), - at least one detector (31, 36; 43; 56, 57) for detecting at least a portion of the measuring radiation that has passed through the optical element (9, 20), as well as - an evaluating device (33; 44; 58) which is connected to the detector (31, 36; 43; 56, 57) and which monitors the temperature and/or temperature-dependent parameter, which is correlated with the intensity of the detected measuring radiation, in a passage region (32, 37) of the measuring radiation based on a predefined relation between the intensity of the detected measuring radiation and the temperature and/or the temperature-dependent parameter in the passage region (32, 37), which relation is based on the temperature-dependent absorption of the transmissive or partially transmissive optical element (9, 20) in the passage region (32, 37),