We report the rate of cosmic ray air showers with multiplicities exceeding 15 muon tracks recorded in the NOvA Far Detector between May 2016 and May 2018. The detector is located on the surface under an overburden of 3.6 meters water equivalent. We observe a seasonal dependence in the rate of multiple-muon showers, which varies in magnitude with multiplicity and zenith angle. During this period, the effective atmospheric temperature and surface pressure ranged between 210 K and 230 K and 940 mbar and 990 mbar, respectively; the shower rates are anticorrelated with the variation in the effective temperature. The variations are about 30% larger for the highest multiplicities than the lowest multiplicities and 20% larger for showers near the horizon than vertical showers.