Following a recent theory suggesting that the local average rate of energy dissipation &egr;rfollows statistics predicted by the gamma distribution rather than the lognormal distribution, the gamma distribution is further examined here as a model for the local temperature dissipation rate &khgr;r. Comparisons of measured moments ⟨&khgr;mr⟩ with those predicted by both the gamma and lognormal distributions clearly favor the gamma model for predicting the power‐law exponents ofr/L. Based on gamma models for both &egr;rand &khgr;r, the bivariate gamma distribution is then examined as a possible model for the joint distribution of dissipation rates &egr;rand &khgr;r. In particular, the bivariate gamma model and the bivariate lognormal model are both compared with the inertial‐range behavior of measured temperature structure functions up to order 12. Some additional comparisons of these models are also made with data involving mixed moments of the velocity and temperature structure functions.