Adiabatic Freestream

I would like to simulate an adiabatic freestream. What is interesting about this is the good validation of the results.
I put two cuboids together for this, whereby the small cuboid is the entry into the room (large cuboid). It would be nice if I could calculate this transiently. Unfortunately, in my experiments so far, this exceeds the possibilities of the sample version. Perhaps I just overlooked something and it is possible after all?
It would also be important for me to be able to mesh the centre of the room more finely than at the edges. I selected a slip function for the walls anyway, so they should not be an obstacle for the free jet. The optimum would be a mesh consisting of cubes that are very small in the middle and get bigger towards the edges. How can I achieve this?

Yours sincerely, Patrick
Here is the project: SimScale