Potential temperatures for opacity set 1 with N_c = 100. Deeper potential and lower opacity lead to a flatter potential temperature profile. Radially, the simulation runs with have flat ϑ-profiles; this does not denote the onset of convection, but rather the action of the horseshoe flows that can freely enter and exit the gravitational well. In z, a steeper profile corresponds to stronger accretion flows from this direction. The much higher values of ϑ result from the low density in the disc atmosphere, as we have r_H≅H_disc throughout our work.