  Seasonal variations of atmospheric muons are traditionally interpreted in
terms of an effective temperature that relates the atmospheric temperature
profile at a given time to the dependence of muon production on atmospheric
depth. This paper aims to review and generalize the treatment of muon
production and effective temperature that has been used to interpret seasonal
variations of atmospheric muons by many experiments. The formalism is developed
both in integral form -- for application to compact detectors at a fixed depth
that record all muons with $E_\mu > E_\mu^\mathrm{min}$ -- and in differential
form -- for application to extended detectors like IceCube, KM3NeT, and
Baikal-GVD, where the rates are proportional to energy-dependent effective
areas.
