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Characterizing the physical conditions at disk scales in class 0 sources is crucial for constraining the protostellar accretion process and the initial conditions for planet formation. We use ALMA 1.3 and 3 mm observations to investigate the physical conditions of the dust around the class 0 binary IRAS 16293–2422 A down to ∼10 au scales. The circumbinary material’s spectral index,α, has a median of 3.1 and a dispersion of ∼0.2, providing no firm evidence of millimeter-sized grains therein. Continuum substructures with brightness temperature peaks ofT_b∼ 60–80 K at 1.3 mm are observed near the disks at both wavelengths. These peaks do not overlap with strong variations ofα, indicating that they trace high-temperature spots instead of regions with significant optical depth variations. The lower limits to the inferred dust temperature in the hot spots are 122, 87, and 49 K. Depending on the assumed dust opacity index, these values can be several times higher. They overlap with high gas temperatures and enhanced complex organic molecular emission. This newly resolved dust temperature distribution is in better agreement with the expectations from mechanical instead of the most commonly assumed radiative heating. In particular, we find that the temperatures agree with shock heating predictions. This evidence and recent studies highlighting accretion heating in class 0 disks suggest that mechanical heating (shocks, dissipation powered by accretion, etc.) is important during the early stages and should be considered when modeling and measuring properties of deeply embedded protostars and disks.