The ability to imagine ourselves in the past, in the future or in different spatial locations suggests that the brain can generate cognitive maps that are independent of the experiential self in the here and now. Using three experiments, we asked to which extent Mental Time Travel (MTT; imagining the self in time) and Mental Space Navigation (MSN; imagining the self in space) shared similar cognitive operations. For this, participants judged the ordinality of real historical events in time and in space with respect to different mental perspectives: for instance, participants mentally projected themselves in Paris in nine years, and judged whether an event occurred before or after, or, east or west, of where they mentally stood. In all three experiments, symbolic distance effects in time and space dimensions were quantified using Reaction Times (RT) and Error Rates (ER). When self-projected, participants were slower and were less accurate (absolute distance effects); participants were also faster and more accurate when the spatial and temporal distances were further away from their mental viewpoint (relative distance effects). These effects show that MTT and MSN require egocentric mapping and that self-projection requires map transformations. Additionally, participants' performance was affected when self-projection was made in one dimension but judgements in another, revealing a competition between temporal and spatial mapping (Experiment 2 & 3). Altogether, our findings suggest that MTT and MSN are separately mapped although they require comparable allo- to ego-centric map conversion.