i would ask how is it possible to add kinematic viscosity and density based on the equations that allow to calculate their value.
In Conjugate Heat Transfer example these quantities are constant. But if i want to get variable quantities based on their equations?
What the idea of the solutions can be? Because these equations involved also the temperature of the flow so, i think, that is not possible to solve flow net first and then thermal net as in the example.

Making these variables a function should be possible. Note that when defining a PDE, many constants in the constructor allow for either a numeric, sympy expression or a string (kinematic viscosity in the N-S equations included).

E.g. in the sympy case: the idea would be to define a sympy expression for your viscosity, feed this expression into the N-S PDE, and then create an additional Node for calculating the viscosity (the from_sympy() function is designed for this. )

What the idea of the solutions can be? Because these equations involved also the temperature of the flow so, i think, that is not possible to solve flow net first and then thermal net as in the example.

I think here you are thinking of having a fully coupled system here (flow depends on thermals, we can avoid this due to the properties of the problem). If thats the case, I would expect the training of the thermal/flow model would have to alternate (train one NN for X iterations then train the other NN for Y iterations and repeat). This is more of a research topic, that would require some experimenting.
The initial state may be tricky.