•Multilayered InGaAs/GaAs QD structures were grown using As2 flux.•Three-dimensional ordering of self-assembled QD arrays was observed.•Nanostructures were studied by TEM, AFM, and photoluminescence.•Observed regularities were explained by competing diffusion and strain on surface.•3D ordering of QDs can be controlled by growth temperature. A comprehensive microscopy analysis has been undertaken to study three-dimensional quantum dot (QD) ordering in multilayered In0.4Ga0.6As/GaAs structures grown with an As2 flux at different substrate temperatures. Atomic force microscopy, transmission electron microscopy, and photoluminescence measurements were employed to fully understand the formation of these extended dot structures. Changes in the lateral pattern of QD ordering are correlated with their vertical alignment. These correlations are analyzed in light of the inherent transformation of the wetting and spacer layers, as well as changes in the shape, strain, and composition of individual QDs. The experimental results are attributed to the anisotropy in the thermally activated surface mass transport and the relaxation of elastic stresses.