Jimbo
I have tried a pad in the Hennessey and so has Quentin.  Quentin usually wakes up in the middle of the pad only under it.  I tried using a pad a couple of times and found it hard to get in the hammock in the sleeping bag and on top of the pad.  You can never have too many canoes or hammocks so I bought a new hammock.  My new one is a BlackBird Warbonnet.  It is a asymmetric so you lay flat and have shoulder room so I can sleep on my side.  It is top entry making it easer to get in and out.  It has a double bottom so your foam pad does not slip around.
All right if inney verses outey is old how about asymmetric verses peapod!

Db
The air definitely sucks more heat then the ground. It can be like sleeping on a cold waterbed with a electric blanket on you. Your body is cold so it produces more heat but the heat does not go to the correct spots.  I can get 1/8 and ¼ foam pads. I would rather deal with the 1/8 if it will do the job.

Marlin and ic
I have used a air mattress in a big Agnes in my Hennessey.  It kept me warm except it was not wide enough where the hammock comes up on the side and rests on your shoulder.  It was too thick and made the hammock not lay as comfortable. If I were on the ground I think the inflatable would be the best.
MagicPaddler