Periodic driving is used to steer physical systems to unique steady states, producing enhanced properties inaccessible to non-driven systems. For open quantum systems, characterizing the steady state is challenging and existing results are generally limited to specific types of driving, such as high frequency. In this talk, I will go beyond this limit by studying a generic periodically driven N-level quantum system interacting with a low-density thermal gas. Exploiting the framework of Floquet scattering theory, we establish general Floquet thermalization conditions constraining the nature of the steady state and the transition rates. Moreover, I will examine theoretically the structure of the steady state at high temperatures, and find out that it complies, rather surprisingly, with the Boltzmann law for any driving. Numerical calculations illustrate our theoretical elaborations for a simple toy model.