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Atmospheric muon neutrinos are produced by meson decays in cosmic-ray-inducedair showers. The flux depends on meteorological quantities such as the airtemperature, which affects the density of air. Competition between decay andre-interaction of those mesons in the first particle production generationsgives rise to a higher neutrino flux when the air density in the stratosphereis lower, corresponding to a higher temperature. A measurement of a temperaturedependence of the atmospheric $\nu_{\mu}$ flux provides a novel method forconstraining hadro\-nic interaction models of air showers. It is particularlysensitive to the production of kaons. Studying this temperature dependence forthe first time requires a large sample of high-energy neutrinos as well as adetailed understanding of atmospheric properties. We report the significant ($>10 \sigma$) observation of a correlation between the rate of more than 260,000neutrinos, detected by IceCube between 2012 and 2018, and atmospherictemperatures of the stratosphere, measured by the Atmospheric Infrared Sounder(AIRS) instrument aboard NASA's AQUA satellite. For the observed 10$\%$seasonal change of effective atmospheric temperature we measure a 3.5(3)$\%$change in the muon neutrino flux. This observed correlation deviates by about2-3 standard deviations from the expected correlation of 4.3$\%$ as obtainedfrom theoretical predictions under the assumption of various hadronicinteraction models

Observation of Seasonal Variations of the Flux of High-Energy Atmospheric Neutrinos with IceCube