mike,
bare with me here... when it gets cold here in florida,(I know not much in comparison to chicago) for or outdoor cats, we have this plastic disk, kinda like a hot water bottle, that we microwave for 10 mins. and it stays warm all night.
Now I know they have some ice pack type things that you freeze and can put on your back. Was wondering if their isn't something similar to these examples that could be microwaved and somehow wraped around.
Obviously they have the stickable hot pads for your back, which would get expensive quick. Perhaps an electric pad might work, but similar expense? You might want to check walmart,target, etc. in the same section for something you could microwave...
You might have to build sometype of rig, to help with weight, since you would not want to put stress on your layer. Also, you might need to put something in between like a cloth, so it doesn't get to hot...
Hope this might help... Good Luck!!!