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A temperature sensor is a sensor whose physical response is used to estimate temperature. A resistance thermometer and a thermistor use changes in electrical resistance; a thermocouple uses the Seebeck effect. The sensor element, its thermal contact and its electrical readout together determine what a temperature measurement means.^[ref]

A contact sensor first responds to its own temperature, which need not immediately equal that of the object or fluid. A useful original lumped thermal model writes the first law of thermodynamics for a sensor with heat capacity $C$, thermal conductance $G$ to an environment at $T_e$, and internal heating power $P$:For constant inputs, its thermal time constant and equilibrium are $\tau =C/G$ and $T_{s,\infty }=T_e+P/G$. The temperature sensor response time and the bias from heating are different properties. Better thermal coupling both shortens $\tau$ and reduces $P/G$ in this model.

Take stipulated values $C=0.020J/K$ and $G=0.010W/K$. Then $\tau =2\mathrm{s}$. With $P=0$ and an environment step from $20$ to $30{}^{\circ }\mathrm{C}$,At $t=2\mathrm{s}$ the sensor reads about $26.32{}^{\circ }\mathrm{C}$, despite a perfect electrical readout. Reaching $90\%$ of the step takes $\tau \ln 10=4.605\mathrm{s}$. A steady $1\mathrm{mW}$ heating input would instead add $0.10\mathrm{K}$ at equilibrium. These are model calculations, not universal sensor specifications.

A proposed two-bath step test of a temperature sensor transfers a small probe between two well-stirred baths with independently established temperatures and records its readout against time. Repeating with a protective sleeve tests the thermal part of the measurement chain. The DOE handbook illustrates insulated sensor elements inside metal sheaths and protective wells; electrical accuracy alone does not describe that complete assembly.^[ref]

Thermal loading by a contact temperature sensor is another limit: a probe exchanges heat with the object and can perturb the quantity it is meant to measure. A small object may require a coupled thermal model rather than a fixed $T_e$. For a resistance thermometer, the excitation also causes Joule heating; checking several currents can distinguish that effect from a fixed readout offset.^[ref]

A two-bath step test of a temperature sensor estimates the dynamic response of a temperature sensor by transferring it between two approximately uniform, stable baths at different temperatures. The apparatus consists of the two baths, independent reference thermometers, a reproducible immersion arrangement, and a recorder fast enough to resolve the temperature sensor response time. Rapid insertion into a liquid at a different temperature is a practical approximation to an instantaneous change in the sensor's surroundings.^[ref]

Let the initial equilibrium be $T_1$ and the second bath be $T_2$. Convert the recorded sensor output to temperature, then form the dimensionless residualFor a single lumped thermal model, $r=e^{-t/\tau }$, so a plot of $\ln |r|$ against elapsed time is a straight line with slope $-1/\tau$. This provides a direct check on the assumed time constant; a curved plot suggests additional response stages or an imperfect input step. The conversion to temperature matters when sensor output is nonlinear.^[ref]

For a constructed example, transfer a sensor from $20{}^{\circ }\mathrm{C}$ into a $60{}^{\circ }\mathrm{C}$ bath. Readings of $40$, $50$, and $55{}^{\circ }\mathrm{C}$ after $2$, $4$, and $6\mathrm{s}$ give residuals $1/2$, $1/4$, and $1/8$. Each successive interval halves the residual, giving $\tau =2/\ln 2\approx 2.89\mathrm{s}$ and $t_{90}\approx 6.64\mathrm{s}$.

Record the transfer delay, immersion depth, stirring conditions, probe sheath and readout filtering with the result. These affect heat transfer or the measured transient. A temperature sensor response time measured in one medium need not apply in another.^[ref]