An AlInN/AlGaN microcavity (MC) containing a GaN/Al0.2Ga0.8N multiple quantum well (MQW) structure is investigated through room temperature (RT) photoluminescence and reflectivity experiments. A vacuum Rabi splitting as large as 50 meV at RT is reported for this MC structure, the highest value reported so far for a semiconductor MC containing QWs. This is shown to result from a geometry combining a state of the art nitride-based MC with a MQW system where the built-in electric field has a reduced impact on the oscillator strength of optical transitions. The contribution of Bragg modes seen in optical spectra is well accounted for by transfer matrix simulations. In addition, the sensitivity of the present system to the tuning between the various optical components of the microcavity (bottom and top Bragg reflectors and active cavity region) to maximize the strong-coupling regime is also shown through simulations. Prospects regarding the nonlinear polariton emission from such a structure indicate that this type of MCs could potentially sustain ultrafast polariton parametric amplification up to 440 K, thanks to an increased exciton binding energy. More generally, it is predicted that, owing to a large exciton saturation density in excess of 1x10(12) cm(-2) per QW, such a MC structure would be suitable for the observation of nonlinear effects associated with cavity polaritons (polariton lasing and polariton Bose-Einstein condensates) at RT and above.