In the canonical view of the neocortical microcircuit, first-order thalamic projections target layer 4 (L4), which in turn projects onto layer 2/3 (L2/3) pyramidal cells (PCs) and then finally onto layer 5 (L5) PCs. Although this is a motif found throughout the neocortex, the functional role of this architecture has remained unclear. Here, inspired by recent observations showing that first-order thalamic input also targets L5 pyramidal cells, we propose that the canonical microcircuit enables the brain to learn through temporal self-supervision. In our model, L2/3 PCs learn to predict thalamic inputs by comparing past sensory information originating from L4 with the current thalamic input received by L5 PCs. First, we tested our model in a simple sensorimotor task, in which visual flow must be associated with motor speed signals. Our model can successfully learn to predict visual flow through local L2/3-L5 self-supervised learning and visuomotor interactions through cortico-cortical learning. When halting the visual input after training, it generates prediction error signals with positive and negative error signals dominating L2/3 and L5, respectively, in line with recent experimental findings. Next, we used the prediction errors generated by L2/3-L5 interactions as intrinsic reward (i.e. surprise) to guide exploration in a reinforcement learning control task. Our results show that agents trained with this form of learning develop a diversity of task-relevant behaviours. Overall, our work proposes that the classical L4->L2/3->L5 motif underlies a form of self-supervised learning in the brain with important functional implications.