Metamaterials have generally been studied by means of the time-harmonic approach, where the wave propagation is described in terms of the spatial coordinates. However, recently studies of temporal metamaterials, where the electromagnetic properties change in time, have been initiated by metamaterials researchers. We therefore use the space-harmonic method to study a 'temporal step' metamaterial. By gradually switching the material parameters in time between two values, the medium can be described using the hyperbolic tangent mathematical function. Exact analytical solutions for the fields are obtained and analyzed. The space-harmonic analysis of temporally graded metamaterials is dual to the time-harmonic analysis of spatially graded metamaterials, that have been extensively studied by the present authors.