An ultrasonic thickness gauge is provided for measuring the thickness of a hot substrate and configured to be permanently installed on the substrate, the ultrasonic thickness gauge comprising: (a) a transducer, the transducer comprising a piezoelectric element for transmitting pulses of ultrasonic vibrations and for receiving pulses of reflected ultrasonic vibrations; (b) a delay line having a first surface attached to the piezoelectric element and a second surface configured to be attached to the substrate; wherein the delay line has a coefficient of thermal expansion (CTE) at 200°C from 4x 10-6/°C to 11 x 10-6/°C, preferably from 5 x 10-6/°C to 11 x 10-6/°C, more preferably from 6 x 10-6/°C to 10 x 10-6/°C.
