What's wrong with convection? What FlowSim can actually offer you over Sim is that is gonna calculate the convection coefficient based on the flow conditions within the channel. But given what I understand of your problem, you can calculate that convenction coefficient with a basic book of Heat Transfer (Fundamentals of heat and mass transfer 7th edition incropera would be my choice) AT WORST.
if the water temp doesn't change much on the way through just put temp BC there. Assuming it is ambient still air put a convection coefficient on the outside of the AA - 5-10 w/m^2K should be close enough. then take the temp distribution into a static analysis.