Thermal Poiseuille flow -- Boundary conditions

I have some problems with open boundary duct flow.

fully developed conditions for temperature and velocity.
using D2Q9 with double distribution functions of He’s model.
I faced some errors at the outlet boundary for temperature profiles.
by the way, I have some problems in mass conservation.

anyone get the results od this problem correctly. would you please tell me which boundary conditions you apply and how?

Thanks for any help, in advanced.