An elongate temperature sensor (10) comprises two electrical conductors (12,14) having temperature sensitive insulating material between them whose resistance and capacitance varies with temperature but according to respectively different known relationships. An alternating waveform (V in ) is applied across the sensor (10) through a known resistor (R s ). The amplitudes of the voltage waveforms developed across the known resistor (R s ) and across the sensor (10) are compared and the phase difference between them measured to determine the corresponding resistance and capacitance values of the sensor (10). The measured value of one parameter is then substituted into the respective known relationship to produce a corresponding temperature value for the sensor (10). This temperature value is then substituted into the relationship for the other parameter to calculate a notional value for that parameter. If that notional value differs from the measured value, this is used to produce an indication that the sensor is not being uniformly heated but has an overheated sectional part. By means of further processing, the length and position of the overheated section and its actual temperature can be determined.