We derive equations for the mean entropy and the mean internal energy in low-Mach-number temperature stratified turbulence (i.e. for turbulent convection or stably stratified turbulence), and show that turbulent flux of entropy is given by F-s = (rho) over bar(us) over bar, where (rho) over bar is the mean fluid density, s is fluctuation of entropy and overbars denote averaging over an ensemble of turbulent velocity fields, u. We demonstrate that the turbulent flux of entropy is different from the turbulent convective flux, F-c = (T) over bar(rho) over bar(us) over bar, of the fluid internal energy, where (T) over bar is the mean fluid temperature. This turbulent convective flux is well-known in the astrophysical and geophysical literature, and it cannot be used as a turbulent flux in the equation for the mean entropy. This result is exact for low-Mach-number temperature stratified turbulence and is independent of the model used. We also derive equations for the velocity-entropy correlation, (us) over bar, in the limits of small and large Peclet numbers, using the quasi-linear approach and the spectral tau approximation, respectively. This study is important in view of different applications to astrophysical and geophysical temperature stratified turbulence.