Dust temperature distribution in the mid-planes of a 3D MC-RT/MHD collapse simulation. Rows show the results of the same model, but of inclinations differing by 90°. In the left column, the dust was heated by 3D MC-RT simulation alone. The middle column shows the dust temperature distribution as a result of MHD shock heating. The dust temperature combined by offset dust heating, as described in Sect. 2.4, is shown in the right column. The length of 1400 AU is for scale. We applied an upper cut-off of 400 K (blue regions) to the mid-plane images for better illustration.