I get the process with uninsulated air mattresses transferring heat due to convection currents when used on the ground, but I'm hoping that hammocks may be a little different. You can start by throwing out the need to support the user's weight and actually pressing down on the mattress surface.
What would happen if you took a big space blanket envelope and filled it with long balloons and put that between the hammock bottom and an outer cover of silnylon? You would have two reflective space blanket surfaces separated by 4" or so of air in a balloon, with a layer of breathable nylon above and a non-breathable layer below, topped off with a compressed sleeping bag layer and a 98.6F heat source.
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