Temperature changes in the simulation. (a) Temporal and height variations in the surface-averaged temperature. (b) Time series of the volume-averaged temperature within [−2, 2] Mm × [−2, 2] Mm × [5, 100] Mm. (c) The solid and dashed black lines depict the height dependence of normalised $\langle {\omega }_z^2\rangle$ and $\langle j_z^2\rangle$, respectively, which are averaged at each height over the time range from t = 0 to 1200 s. The solid blue line represents the increase in surface-averaged temperature (ΔT) relative to t = 0 as a function of heights, with the dotted blue line corresponding to ΔT = 0.