Mike -
We too have a 2400SE and our aft storage area either came insulated from the factory, or the previous owner installed it. Ours is lined with 1" foam held tightly with what looks like double sided tape. I've used it as a cooler once.
The only downside is the small drainhose empties into the bilge, right on top of the back of the motor, which doesn't thrill me. I could re-route the hose to something thru-hull above the water line, but we store our fenders/lines/boathook in there. I only wish it was big enough to hold the magna grill!