The distributed temperature sensor employs an optical fibre (1) as sensing element located in an ambient or near a body of which the temperature is to be monitored or measured. A source (3) of light pulses sends into the fibre 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 computing means obtains the temperature from said variations. The source (3) and the spectrum variation analyzing means (9) 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 fibre.