= Temperature sensor
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.<DOE Fundamentals Handbook Instrumentation and Control Volume 1 of 2>[Module 1, printed pp. 1–7, resistance detectors and thermocouples]{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 $P$:
$$
C\frac{dT_s}{dt}=G(T_e-T_s)+P.
$$
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 $C=0.020\,\mathrm{J/K}$ and $G=0.010\,\mathrm{W/K}$. Then $\tau=2\,\mathrm s$. With $P=0$ and an environment step from $20$ to $30\,{}^\circ\mathrm C$,
$$
T_s(t)=30-10e^{-t/(2\,\mathrm s)}\quad\text{in degrees Celsius}.
$$
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 \b[$\tau\ln10=4.605\,\mathrm s$]. 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.<DOE Fundamentals Handbook Instrumentation and Control Volume 1 of 2>[Module 1, pp. 3–4, Figures 2–3, element, sheath and protective well]{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.<Guide on Secondary Thermometry: Industrial Platinum Resistance Thermometers by Jonathan Pearce and others>[§4.1, self-heating and excitation-current dependence]{ref}
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