We consider 4D shape reconstructions in multi-view environments and investigate how to exploit temporal redundancy for precision refinement. In addition to being beneficial to many dynamic multi-view scenarios this also enables larger scenes where such increased precision can compensate for the reduced spatial resolution per image frame. With precision and scalability in mind, we propose a symmetric (non-causal) local time-window geometric integration scheme over temporal sequences, where shape reconstructions are refined framewise by warping local and reliable geometric regions of neighboring frames to them. This is in contrast to recent comparable approaches targeting a different context with more compact scenes and real-time applications. These usually use a single dense volumetric update space or geometric template, which they causally track and update globally frame by frame, with limitations in scalability for larger scenes and in topology and precision with a template based strategy. Our templateless and local approach is a first step towards temporal shape super-resolution. We show that it improves reconstruction accuracy by considering multiple frames. To this purpose, and in addition to real data examples, we introduce a multi-camera synthetic dataset that provides ground-truth data for mid-scale dynamic scenes.