Abstract
If the gauge quantum chiral anomaly predicts chiral effects related to chemical potentials, then the gravitational chiral anomaly is responsible for the effects of temperature. The prediction of the gravitational anomaly for the temperature term in the chiral vortical effect coincides with the prediction of statistical calculations by the Kubo formula for spin 1/2, but two predictions disagree already for spin 1. A solution to this problem related to the features of infrared regularization is described. Also the thermodynamic instability in systems with acceleration, which occurs at temperatures below the Unruh temperature and the transition through the Unruh temperature are discussed.
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