Remember that even at indoor temps you'll probably need some sort of under insulation like an under quilt or a closed cell foam pad.
With double layer hammocks you could insert a thin CCF pad between the layers. I'm just guessing here, but a thin pad should be enough for indoor temps (down to 60F) yet not as uncomfortable as the thicker pads used outdoors, like the classic blue pad from Walmart.
Under quilts are very comfortable and work great but they also complicate things more. Personally I use UQ's.
Glad to hear there's an MD out there who sees the benefits of sleeping in a hammock.