There's nothing containing the air inside the duct. Thus, it will expand to ambient pressure. As the air is heated, this means it will expand to a slightly greater volume - but it will still expand to ambient. In effect, you get a slight thrust increase from the heating of the air, just as in a ram engine.
As a sidenote, the heat exchanger under the P51 Mustang will often contribute
thrust due to the design of the duct and the heating of the air inside it. Ram engine...
I thought I was doing good trying to avoid those airport hotels... and look at me now.