Resistance calibration and monitoring of thermal systems

A method of measuring a temperature of a heater, the heater comprising a resistive element comprising a material with a Curie temperature, the resistive element including an end joined to at least one of power leads that has a material different from the material of the resistive element such that a thermocouple junction is formed between the resistive element and the at least one of the power leads for measuring the temperature of the heater, the method comprising:

• generating a standard resistance-temperature (R-T) curve for the resistive element of the heater to identify values of the R-T curve and an inflection point at the Curie temperature, the standard R-T curve being generated when the resistive element is in isothermal conditions;
• generating operational R-T curves for the resistive element over an operational time period during a normal operation of the heater in which the resistive element is non-isothermal due to a heat loss at the end of the resistive element;
• comparing the standard R-T curve to the operational R-T curves;
• adjusting the operational R-T curves to the standard R-T curve at the Curie temperature to obtain adjusted operational R-T curves;
• measuring the temperature of the heater by the thermocouple junction;
• and
• calculating a revised temperature of the resistive element based on the adjusted operational R-T curves and the temperature measured by the thermocouple junction to compensate for the heat loss at the end of the resistive element.

A method of measuring a temperature of a heater, the method comprising:

• generating a standard resistance-temperature (R-T) curve for the resistive element to identify values of the R-T curve and an inflection point at the Curie temperature, the standard R-T curve being generated when the resistive element is in isothermal conditions, the resistive element having an end joined to a power lead made of a material different from the material of the resistive element to form a thermocouple junction therebetween;
• generating operational R-T curves for the resistive element over an operational time period during a normal operation of the heater;
• developing mathematical representations of shapes of the R-T curves;
• adjusting the operational R-T curves to the standard curve at the Curie temperature based on the mathematical representations to obtain adjusted operational R-T curves;
• measuring the temperature of the heater by the thermocouple junction;
• and
• revising the temperature of the heater obtained by the thermocouple junction based on the adjusted operational R-T curves to obtain a revised temperature that compensates for a heat loss at the end of the resistive element.