@grosua great that you made 3 simulations, i think you are good along the way.
For run 1: i noticed indeed the shaky T1 convergence, luckily you seemed to have solved that by the relaxation factor, thanks for the support person that suggested that. Though it did cross my mind before too. T1 you saw is not the max I observed in paraview: I made 3 slices at height: 0.25, 1.5 and 3 and reported values are approximately 450, 400 and 400, except for the peak. There I do see just a very small area with a peak T1 value see figure below
Maybe running more iteration might resolve this problem. I am trying to figure out what might cause this. The boundary condition is the one from the original project, however a fixed value for the passive scalar is set. I am not sure if this is a proper boundary condition. I tried running inlet-outlet type boundary conditions but those did not converge so I just suggest to stick to the original bc and continue with these results, perhaps running more iterations.
Regarding mesh refinement let’s just stick to the current mesh, including more refinement at your inlet, also if the support person suggested that too.
The values in run 2 seem half of the values of run 1, however the flow field is also significantly different, because the flow field has converged more (4k in run 2 vs 2k in run 1). So it is natural that T1 is going to be differen too.
Personally, before continuing I would rather check if your velocities do converge depending on number of iteration. If your velocity changes by 10% if you add a few k more iteration, i would really suggest to do more iterations as you may imagine that makes more sense.
For post processing , I am having difficulty with the in-browser post processor, so I strongly advice paraview.
Maybe it is good to see how the velocity profile along a fixed line develops with increasing number of iterations, and see if it converges truly, before deciding what is a good number of iteration, because the flow field is really what decided the values for T1 at the end.
PS: If you need any help on post processing in paraview let me know, so I could help you out with that perhaps. Regarding values, I think you are going in the good direction with Run 2 and Run 3, even if the values are oscillatory, the order of magnitude of T1 has decreased to lower values, than we were initially at (1e-2). That is important of course.