Yes, you can simulate all of those factors.
You can import Flow data into Simulation (Flow will do the heat calculations also, you do not need to do a separate thermal simulation). And Simulation can determine if the thermal expansion forces are acceptable.
Whether you need static or time dependent depends on what you are looking for (how fast does it heat vs does the airflow produce uniform temperatures).
The wood heat source you would have to determine the energy content and burn rate to approximate the heat source quantity.