  We investigate superradiant enhancements in the refrigeration performance of
a set of $N$ three-level systems that are collectively coupled to a hot and a
cold thermal reservoir and are additionally subject to collective periodic
(circular) driving. Assuming the system-reservoir coupling to be weak, we
explore the regime of stronger periodic driving strengths by comparing
collective weak driving, Floquet-Lindblad, and Floquet-Redfield master
equations. We identify regimes where the power injected by the periodic driving
is used to pump heat from the cold to the hot reservoir and derive analytic
sufficient conditions for them based on a cycle analysis of the
Floquet-Lindblad master equation. In those regimes, we also argue for which
parameters collective enhancements like a quadratic scaling of the cooling
current with $N$ can be expected and support our arguments by numerical
simulations.
