NOVELTY - A multi-mode optical waveguide fiber (F1) comprises central core region having outer radius (ra), surrounded by an inner cladding region having an outer radius (ric), where the inner cladding region has lower index of refraction than the central core region, where both the central core region and the inner cladding region are doped with fluorine, where the fiber has an overfilled Modal Bandwidth of greater than 500 MHz.km at a wavelength of 850-1300 nm, according to IEC 60793-2-10.    USE - As a multi-mode optical waveguide fiber, used at elevated temperature, such as at a temperature 150 degrees C and preferably in an environment with increased hydrocarbon and/or hydrogen content, such as in an oil well, in a gas well, and in a geothermal application; for sensing, such as temperature sensing; and in distributed temperature sensor system (claimed). Also useful for communication over shorter distances, such as within a building or on a campus; and for backbone applications in buildings.    ADVANTAGE - The fiber has an absolute change in attenuation of signal light at a 1200-1550 nm of less than 0.5 (preferably less than 0.3) dB/km, for the following conditions, where the fiber is maintained for 5 days at 70 degrees C in an inert atmosphere containing 1 vol.% hydrogen, and is annealed for 6 days at 70 degrees C in an atmosphere of air. The multi-mode optical waveguide fiber is much less expensive than single-mode optical fiber; and has high capacity and reliability.    DETAILED DESCRIPTION - A multi-mode optical waveguide fiber (F1) comprises central core region having outer radius (ra), surrounded by an inner cladding region having an outer radius (ric), where the inner cladding region has lower index of refraction than the central core region, where both the central core region and the inner cladding region are doped with fluorine, where the refractive index profile of the central core region is of the gradient index type and central core region of 0-ra contains germanium at a maximum concentration of 0.5-4 wt.% taken at a given radius, where the fiber has an overfilled Modal Bandwidth of greater than 500 MHz.km at a wavelength of 850-1300 nm, according to IEC 60793-2-10. INDEPENDENT CLAIMS are included for the following:    (1) a method of sensing, such as temperature sensing, involving providing the multi-mode optical waveguide fiber (F1), and transmitting an optical signal through the fiber; and    (2) a distributed temperature sensor system comprising: a pulsed light source for emitting short pulses of light with a narrow bandwidth about an excitation frequency (w); the multi-mode optical waveguide fiber (F1), having an input end, where the input end is disposed to receive pulses of light emitted from the pulsed light source; beamsplitter disposed in-between the light source and the input end of the fiber; a time domain analyzer for analyzing, as a function of time elapsed since a pulse of light is emitted by the pulsed light source, the spectral components of back scattered light emitted by the input end of the fiber in response to the pulse of light impinging on the input end, where the beamsplitter is disposed to direct the back scattered light emitted from the input end into the time domain analyzer, thus producing time-resolved spectral information, where the time domain analyzer uses the time-resolved spectral information to determine the distribution of temperature along the length of the fiber.