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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 temperature sensor response time specifies how long a temperature sensor takes to complete a stated fraction of its response to a change in the surrounding temperature. The fraction and the test conditions are part of the specification: a 90% response time and a 63.2% response time describe different points on the same record. Rapid immersion in a different-temperature liquid approximates the required step input.^[ref]

For a lumped thermal model with sensor heat capacity $C$, constant thermal conductance $G$ to a bath at $T_b$, and negligible internally generated heat, the energy conservation equation and its solution areThus the time constant $\tau$ is the time to complete $1-e^{-1}\approx 63.2\%$ of the change. The time to complete a fraction $f$ is $t_f=-\tau \ln (1-f)$, so $t_{90}=\tau \ln 10$, whereas the elapsed time between 10% and 90% is $\tau \ln 9$. For example, $\tau =3\mathrm{s}$ gives $t_{90}\approx 6.91\mathrm{s}$ and $t_{99}\approx 13.82\mathrm{s}$.

A two-bath step test of a temperature sensor tests this exponential function model rather than assuming it. Several internal heat capacity elements, a protective sheath, or electronic filtering can produce several response stages. The thermometry guide reports fast and slow components in tested platinum thermometer assemblies; a single quoted time constant need not describe their entire approach to equilibrium.^[ref]