Over the last decades, metamaterials have mostly been studied using the time-harmonic approach, with wave propagation described in terms of the spatial coordinates. The metamaterials community has only recently initiated studies of temporal metamaterials, with electromagnetic properties that change in time. In this work, we propose the space-harmonic method to study a "temporal multistepped"metamaterial. By alternating the material parameters in time, the medium can be described using periodic mathematical functions. The exact analytical solutions for the fields in temporally periodic metamaterials are then obtained. The space-harmonic analysis of temporally periodic metamaterials is dual to the time-harmonic analysis of spatially periodic metamaterials, previously studied by one of the present authors.