We demonstrate that reflectionless propagation of electromagnetic waves between two different materials can be achieved by designing an intermediate temporal medium, which can work in an ultra-wide frequency band. Such a temporal medium is designed with consideration of a multi-stage variation of the material's permittivity in the time domain. The multi-stage temporal permittivity is formed by a cascaded quarter-wave temporal coating, which is an extension of the antireflection temporal coating by Pacheco-Peña et al. [Optica7, 323 (2020)10.1364/OPTICA.381175]. The strategy to render ultra-wideband antireflection temporal medium is discussed analytically and verified numerically. In-depth analysis shows that the multi-stage design of the temporal media implies a continuously temporal variation of the material's constitutive parameters, thus an ultra-wideband antireflection temporal medium is reasonably obtained. As an illustrative example for application, the proposed temporal medium is adopted to realize impedance matching between a dielectric slab and free space, which validates our new findings.