  Even in the absence of resolved flares, the corona is heated to several
million degrees. However, despite its importance for the structure, dynamics,
and evolution of the solar atmosphere, the origin of this heating remains
poorly understood. Several observational and theoretical considerations suggest
that the heating is driven by small, impulsive energy bursts which could be
Parker-style "nanoflares" (Parker 1988) that arise via reconnection within the
tangled and twisted coronal magnetic field. The classical "smoking gun"
(Klimchuk 2009; Cargill et al. 2013) for impulsive heating is the direct
detection of widespread hot plasma (T > 6 MK) with a low emission measure. In
recent years there has been great progress in the development of Transition
Edge Sensor (TES) X-ray microcalorimeters that make them more ideal for
studying the Sun. When combined with grazing-incidence focusing optics, they
provide direct spectroscopic imaging over a broad energy band (0.5 to 10 keV)
combined with extremely impressive energy resolution in small pixels, as low as
0.7 eV (FWHM) at 1.5 keV (Lee 2015), and 1.56 eV (FWHM) at 6 keV (Smith 2012),
two orders of magnitude better than the current best traditional solid state
photon-counting spectrometers. Decisive observations of the hot plasma
associated with nanoflare models of coronal heating can be provided by new
solar microcalorimeters. These measurements will cover the most important part
of the coronal spectrum for searching for the nanoflare-related hot plasma and
will characterize how much nanoflares can heat the corona both in active
regions and the quiet Sun. Finally, microcalorimeters will enable to study all
of this as a function of time and space in each pixel simultaneously a
capability never before available.
