From AMS Glossary
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As used by C. W. Thornthwaite in his 1948 climatic classification, a function of temperature designed to have low magnitude under cold conditions, increasing exponentially with increasing temperature. For a given station, it is numerically equal to the sum of the 12 monthly values of the expression
where t is the normal monthly temperature in °C.
The heat index is used in the computation of potential evapotranspiration, which, in turn, is one of the basic parameters of the 1948 classification.
Thornthwaite, C. W. 1948. An approach toward a rational classification of climate. Geogr. Rev.. 38. 55–94.