While initially, sensing temperature may seem like a simple concept (and it's been getting done for a very long time now) the actual details of what we are sensing can become quite confusing. In its most basic sense, temperature is a measure of the movement of molecules within a body of matter. That matter can be solid liquid or gas, and more frequent movements translate to higher temperatures (with absolute zero at the bottom of the scale, meaning no particle movement at all) The reasons we care about temperature are varied, but mainly we want to be comfortable or we want to ensure that a certain process is happening by manipulating the temperature. Of course our perception of comfort is based on our own sensing of temperature by biological processes far more complex than the processes we use to quantify temperature.
Obviously the thermometer is the simplest way to sense and understand temperature. We figured out pretty early on that certain fluids expand when they are heated, so that their volume is a function of temperature. By controlling and marking this expansion of volume we were able to quantify temperature. As John points out, we were later able to recognize the same principle applies to solids, and we began to use this to control the movment of thin metal strips, which would in turn control some basic circuitry, mainly for switching on and off some electrical process. Of course, this is the principle by which most early thermostats operated.
As we progressed in knowledge of electrical properties of materials, it was found that the resistance of certain conductive materials decreases as we increase the temperature, and so we developed thermistors made of ceramics or polymers to effectively convert a change in temperature to a change in resistance that could be easily measured. We also knew that the current changes between to metals at different temperatures, so a slightly more complicated Thermocouple circuit was developed, where this change in current can be measured across dissimilar metals. Furthermore we found that different metals behaved more predictably for certain temperature ranges, so a number of sets of metals were used for varying applications. Finally, the resistance in a coiled wire was found to be more accurately measurable, so RTD's (made of a homogeneous wire wrapped around a ceramic core) became prominent. These could be configured differently to accomodate different temperature ranges and provided high accuracy and repeatability.
Mike does a great job of explaining the usefulness of all of the sensors mentioned above. However, there are still some applications in which even RTD's and Thermocouples cannot be used. For example measuring the surface temperature of an object that is moving or one that cannot be disturbed becomes quite difficult with the sensors mentioned above. Rather than measuring a change in a specific material's response to a temperature, Pyrometers are able to measure a temperature directly as a function of an object's electromagnetic radiation. The methods by which this is acheived can become rather complex, but in their simplest form all pyrometers consist of a lense to concentrate radiation into a point or array of points and an absorber, which chemically translates radiation into terms of flux. It is at this point that the line between sensing and transducing becomes blurred for me. David gives a good explanation of these principles as applied to an array of infrared sensors (thermography). By some means of transduction the radiation is translated to thermal energy and the thermal energy is translated to an electrical current. The figure below helps explain the process.
References:
http://drexel.summon.serialssolutions.com/search?s.q=thermal+radiation+sensor
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