A resistance thermometer is a passive probe; it requires the passage of a measuring current in order to produce a useful signal. This measuring current heats the element and raises its temperature. Errors will result unless the additional heat is absorbed.

In order to evaluate the measurement error as a function of the current injected through the resistive element, the self-heating coefficient has been defined. The units of the self-heating coefficient are °C/W. As a first approximation, the temperature measurement error is inversely proportional to the power injected into the resistor. Electrical power is calculated according to the following formula: P = R*I². The greater this coefficient, the greater the measurement error for a given current and experimental conditions.

To reduce the error due to this effect, under given conditions, we generally try to reduce the measurement current, but we can’t avoid it. As mentioned above, operating conditions can strongly influence this phenomenon. When temperature measurements are made on a moving fluid, this coefficient decreases with fluid flow speed, as the fluid carries away more and more heat.

From a normative point of view, the IEC60751 standard prescribes the conditions for evaluating this phenomenon. According to this standard, this phenomenon can be quantitatively evaluated in an air stream or in a water stream. In air, the temperature must be between 0 and 30°C, with an air speed of (3 +/- 0.3) m/s. In water, the velocity must be greater than 0.2 m/s. A probe based on a platinum resistive element must not have an error due to self-heating greater than 25% of the standard tolerance class. In practice, the measurement current for Pt100 probes (100 Ohm resistance at 0°C) rarely exceeds 1 mA. As an example, we’ll take a self-heating coefficient value of 20°C/W. For a current of 1 mA and a temperature of 0°C, the power injected into the resistor is [ R*I² = 100 * 1/1000 * 1/1000 * Ω * A * A = 10-4 W ]. This corresponds to a temperature rise of 0.002°C. If the measurement current is 5 mA, the power would be 2.5*10-3 W and the temperature change due to this current would be 0.05 °C.

NB, the resulting error is inversely proportional to the capacity of the thermometer to dispose of the additional heat; this depends on the thermometer materials, construction and environment.

The worst case occurs when a high-value resistor is in a small body. Film RTDs, with little surface area to absorb heat, are a case in point.

Self-heating also depends on the medium in which the thermometer is immersed. The error in still air can be 100 times greater than in moving water.