Modelling a pipe flow with different inlet temperatures
 

I am modelling a simple pipe flow with Re about 50 000. The air flowing into pipe is not in uniform temperature. I have approximated the problem by dividing the inlet into four parts for which I give different inlet temperatures.

When I look at my Fluent solution at a distance of 3 diameters from the inlet the temperature differences are practically the same than at the inlet. According to my intuition there is mixing of the air due to the turbulence, and therefore somewhat more uniform temperature distribution should be achieved.

I have naturally included the energy equation, is there something else that has to be turned on? Could the problem be caused by the RANS decomposition that only calculates the average quantities?