The distributed temperature sensor employs an optical fiber as sensing element located in an ambient or near a body of which the temperature is to be monitored or measured. A source of light pulses sends into the fiber, pulses of predetermined duration. The backscattered radiation is collected for each pulse and the frequency spectrum variations in the backscattered radiation with respect to the incident radiation are analyzed. A computer obtains the temperature from said variations. The source and the spectrum variation analyzer are part of an optical time domain reflectometer which allows the temperature information to be associated with the information on the position of the backscattering point along the fiber.