The IceCube Neutrino Observatory detects atmospheric muon neutrinos above 100 GeV at a rate of about 100 000 per year. These neutrinos originate from decays of charged pions and kaons in cosmic ray air showers. Their flux depends on the probability of production and decay of the parent mesons, and is thus sensitive to the stratospheric temperature. Neutrino rates from 8 years of operation of the detector are correlated with the atmospheric temperature profile as measured by the Atmospheric Infrared Sounder (AIRS). An analysis of this correlation provides a test of models of hadronic interactions in atmospheric air showers. This analysis of neutrinos complements the analysis of the correlation of atmospheric muons with temperature that is presented in another paper at this conference.