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A microcalorimeter (literally, a very sensitive calorimeter) is an instrument that measures very small amounts of heat, in some cases to measure the energy of individual photons. A method of measuring heat is to add it to an object that was in equilibrium with a second object with a much greater heat-storage capacity, then measure the heat flow from the first to the second. Such a configuration can be set up so that the amount of heat flow is evident from the time it takes for the objects to return to some equilibrium-threshold. Such microcalorimeters are one type of instrument used to measure the photon-energy of high-energy photons (e.g., X-ray photons), measuring the heat energy resulting from absorbing such a photon (X-ray microcalorimeter).
Laboratory microcalorimeters are used in producing and studying spectral lines within the X-ray band. In modern astronomy, arrays of microcalorimeters are now available, manufactured as integrated circuits, e.g., for X-ray telescopes. Their technology is very much the same as the analogous arrays of bolometers, such as transition edge sensors or SQUIDs. My impression is that the term microcalorimeter is generally used for short-wavelengths (e.g., X-rays) in which measure and record the heat from individual photons (yielding its photon energy, thus its wavelength), and the term bolometer is used for sensors for longer wavelengths that measure the power of the absorbed EMR, but not by measuring photons individually.