Lid at Liquid to Air Interface - Flow Simulation

I am trying to model water in a cup that is heated by a heater on the bottom of the cup. I set it up as an external study because I want to include in the results the cooling of the cup by natural convection of air around the cup. I have a part in the assembly above the liquid (a lid), in order to set up the fluid subdomain.

What is the best way to set up the lid so it has little to no impact on the study and I get as close as I can come to natural convection of air on the surface of the liquid? Should I make it extra thin and set it as a solid material with properties close to those of air? Is there a boundary condition I can apply to the bottom of this lid that will make it essentially not part of the study?

Perhaps there's a better approach to this altogether. Please let me know your advice.

Thanks.

SolidworksSimulation