All results are from time = 2.5 milliseconds.
Time step is 2E-05 seconds, and the mesh size is 500x20. Metric units are used.

Initial conditions: P = U= 0, T=300K.

Velocity and temperature are increasing uniformly at the inlet (left b.c).

Implicit formulation is used and the unsteady formulation is 2nd-order implicit.
Everything else is the same, the only difference is being pressure based or density based.
Looking at the temperature profile from the pressure based solution, it can be seen that the value at the inlet B.C is implemented. However, the temperature drops quickly in the next node.
Pressure profile

Velocity profile
density profile
Temperature profile