Following the previous works by Maekawa et al. (1991) and Kawada et al. (1991), some turbulence statistics including the triple velocity-temperature correlations were measured in a turbulent boundary layer with a constant temperature for a spanwise direction. Examination was given to the turbulent heat flux budget and also to the reliability of some existing turbulence models. It was revealed that there are remarkable discrepancy between the predicted triple velocity-temperature correlations by the gradient-type model (Launder (1978)) and the experimental result. However, the examination for the turbulent heat flux budget clarified that the budget lies in near local equilibrium except for the near-wall region. Thus, the reliability of the pressure-temperature gradient correlation model is found to be rather important for the prediction of the spanwise turbulent heat flux. The prediction performance of the pressure-temperature gradient correlation model was investigated using two kinds of the models (Launder (1975)), Maekawa et al. (1979). It was found that predicted values by these models show good agreement with the experimental result.