It seems from the Nature paper that what we see is a temperature variation map with the darkest and the brightest regions representing a temperature difference of $\sim 10 \%$ of the mean temperature (remember, though, that by Wien's displacement law, temperature and brightness are connected, so in some sense it is also a brightness map). The temperature/brighness variations are then interpreted as a nonuniform layer of clouds covering the Brown Dwarf atmosphere and partly obscuring the emission from deeper, hotter layers.
From the Nature paper:
Our data clearly show spectroscopic variability intrinsic to Luhman 16B, and this brown dwarf’s rapid rotation allows us to produce the global surface map shown in Fig. 2 using Doppler imaging techniques, . This produces a map that shows a large, dark, mid-latitude region, a brighter area on the opposite hemisphere located close to the pole and mottling at equatorial latitudes.
Looking a bit into the sources about the Doppler Imaging technique, it seems that this is not direct imaging (we do not have the spatial resolution now or in a foreseeable future), but rather a model acquired by maximum-likelihood inference techniques applied on the time variation of the line shapes in the spectra of the Brown Dwarfs.
When a completely isotropic spherical light source rotates, it will give a perfectly symmetric Doppler broadening of its spectral lines due to the velocity difference between the receding and the approaching side of the source. If there are variations in the surface brightness, this will be seen as a variation in the line shape as the darker area moves from blue- to redshifted.
Without having read the full paper, my guess would be that they would then parametrize the surface brightness by amplitudes of a suitable set of spherical harmonics and fit the observed line profile changes to these to acquire a maximum likelihood model which will then be their "heat map".