One key aspect of spatially aware robots is the ability to "find their bearings", ie. to correctly situate themselves in previously seen spaces. In this work, we focus on this particular scenario of continuous robotics operations, where information observed before an actual episode start is exploited to optimize efficiency. We introduce a new model, Kinaema, and agent, capable of integrating a stream of visual observations while moving in a potentially large scene, and upon request, processing a query image and predicting the relative position of the shown space with respect to its current position. Our model does not explicitly store an observation history, therefore does not have hard constraints on context length. It maintains an implicit latent memory, which is updated by a transformer in a recurrent way, compressing the history of sensor readings into a compact representation. We evaluate the impact of this model in a new downstream task we call "Mem-Nav". We show that our large-capacity recurrent model maintains a useful representation of the scene, navigates to goals observed before the actual episode start, and is computationally efficient, in particular compared to classical transformers with attention over an observation history.