  We study little red dots (LRD) detected by JADES and covered by the SMILES
MIRI survey. Our sample contains 31 sources, $\sim70$% detected in the two
bluest MIRI bands, 40% in redder filters. The median/quartiles redshifts are
$z=6.9_{5.9}^{7.7}$ (55% spectroscopic). We analyze the rest-frame ultraviolet
through near/mid-infrared spectral energy distributions of LRDs combining
NIRCam and MIRI observations, using a variety of modeling techniques that
include emission from stars, dust, and (un)obscured active galactic nuclei
(AGN). The NIRCam$-$MIRI colors, for $\geq10$ $\mu$m, are bluer than direct
pure emission from AGN tori; the spectral slope flattens in the rest-frame
near-infrared, consistent with a 1.6 $\mu$m stellar bump. Both observations
imply that stellar emission makes the dominant contribution at these
wavelengths, expediting a stellar mass estimation: the median/quartiles are
$\log \mathrm{M_\star/M_\odot}=9.4_{9.1}^{9.7}$. The number density of LRDs is
$10^{-4.0\pm0.1}$ Mpc$^{-3}$, accounting for $14\pm3$% of the global population
of galaxies with similar redshifts and masses. The flat ultraviolet spectral
range is dominated by young stars. The rest-frame near/mid-infrared (2-4
$\mu$m) spectral slope reveals significant amounts of dust (bolometric stellar
attenuation $\sim3-4$ mag) heated by strong radiation fields arising from
highly embedded compact sources. Our models imply $<0.4$ kpc heating knots,
containing dust-enshrouded OB stars or an AGN producing a similar radiation
field, obscured by $\mathrm{A(V)}>10$ mag. We conclude that LRDs are extremely
intense and compact starburst galaxies with mass-weighted ages 5-10 Myr, very
efficient in producing dust, their global energy output dominated by the direct
and dust-recycled emission from OB stars, with some contribution from obscured
AGN in the mid-infrared.
