A process for precisely measuring a thickness, and optionally thereby corrosion rate, of a metal wall of a vessel or pipe exposed to varying temperatures on at least one of the inside or outside, where the process comprises: a) installing an ultrasonic sensor to a location of the wall where the ultrasonic sensor includes an ultrasonic source disposed to provide an ultrasonic pulse into the wall, an ultrasonic receiver disposed to receive reflections of the ultrasonic pulse from the opposite side of the wall, a temperature sensor and analytical circuitry to receive and collect temperature data from the temperature sensor and waveform data from the receiver; b) measuring the temperature of the wall; c) emitting a series of pulses from the ultrasonic source into the wall; d) receiving at least a first and second reflection of each pulse from the wall that has crossed the thickness of the wall with a receiver to create a wave and collecting the waveforms into a Sample Collection; e) aligning the waveforms within the Sample Collection; f) averaging the set of aligned waveforms within the Sample Collection to create a Representative Waveform for the Sample Collection; g) identifying at least first and second echo sets within the Representative Waveform representing the first reflection from the wall and second reflection from the wall, respectively; h) determining the characteristics points of each backwall echo; i) averaging the characteristic points of each backwall echo to calculate a representative location of the backwall echo; j) determining the thickness of the wall based on the precise time for an ultrasonic sound wave to travel through the wall; and k) wherein the process further includes the step of calculating a coefficient of thermal velocity expansion for the metal wall by collecting a number of Sample Collections at different temperatures performing a regression analysis for the various thickness measurements at the temperature of the respective Sample Collections to find a coefficient of thermal velocity expansion for the metal wall and thereafter provide temperature corrected thickness measurements of the metal wall.; a) installing an ultrasonic sensor to a location of the wall where the ultrasonic sensor includes an ultrasonic source disposed to provide an ultrasonic pulse into the wall, an ultrasonic receiver disposed to receive reflections of the ultrasonic pulse from the opposite side of the wall, a temperature sensor and analytical circuitry to receive and collect temperature data from the temperature sensor and waveform data from the receiver; b) measuring the temperature of the wall; c) emitting a series of pulses from the ultrasonic source into the wall; d) receiving at least a first and second reflection of each pulse from the wall that has crossed the thickness of the wall with a receiver to create a wave and collecting the waveforms into a Sample Collection; e) aligning the waveforms within the Sample Collection; f) averaging the set of aligned waveforms within the Sample Collection to create a Representative Waveform for the Sample Collection; g) identifying at least first and second echo sets within the Representative Waveform representing the first reflection from the wall and second reflection from the wall, respectively; h) determining the characteristics points of each backwall echo; i) averaging the characteristic points of each backwall echo to calculate a representative location of the backwall echo; j) determining the thickness of the wall based on the precise time for an ultrasonic sound wave to travel through the wall; and k) wherein the process further includes the step of calculating a coefficient of thermal velocity expansion for the metal wall by collecting a number of Sample Collections at different temperatures performing a regression analysis for the various thickness measurements at the temperature of the respective Sample Collections to find a coefficient of thermal velocity expansion for the metal wall and thereafter provide temperature corrected thickness measurements of the metal wall.;