  For a standard two-level atom coupled to the quantized field of a resonant
cavity, finite temperature effects lead to thermal occupation of the cavity
modes that obfuscates measurement of the quantum nature of the atom-light
interaction. In this paper we demonstrate that using a hybrid system of a
superconducting cavity coupled to a multi-level Rydberg atom it is possible to
observe the quantum nature of strong coupling even at finite temperatures, and
to exploit this coupling to permit cooling of the thermal microwave mode
towards the ground-state, enabling observation of coherent vacuum Rabi
oscillations even at 4~K for realistic experimental parameters. Cooling for
multiple atoms is also explored, showing maximal cooling for small samples,
making this a viable approach to cavity cooling with potential applications in
long-range coupling of superconducting qubits via thermal waveguides.
