The combined temperature-humidity heat stress is estimated in farm animals by indices derived of an index based on human thermal comfort sensation. The latter index consists of temperature and humidity measures that sum to form the temperature-humidity index (THI). The hitherto unknown relative contribution of temperature and humidity to the THI was examined. A temperature-humidity data set (temperature 20–42 °C and relative humidity 10–70 %) was used to assess by regression procedures the relative weights of temperature and humidity in the variance of THI values produced by six commonly used heat stress indices. The temperature (Ta) effect was predominant (0.82–0.95 of variance) and humidity accounted for only 0.05 to 0.12 of THI variance, half of the variance encountered in animal responses to variable humidity heat stress. Significant difference in THI values was found between indices in the relative weights of temperature and humidity. As in THI indices, temperature and humidity are expressed in different physical units, their sum has no physical attributes, and empirical evaluations assess THI relation to animal responses. A sensible heat THI was created, in which at higher temperatures humidity reaches 0.25 of sensible heat, similarly to evaporative heat loss span in heat stressed animals. It relates to ambient temperature-humidity similarly to present THI; its values are similar to other THI but greater at higher humidity. In warm conditions, mean animal responses are similar in both indices. The higher sensitivity to humidity makes this index preferable for warm-humid conditions. © 2016, ISB.