I changed the battery yesterday and the old battery had this sleeve around it. Not a heater. Not a lot of foam to insulate, more like foam weather stripping around the top edge. It sloped down in front so one could see the battery acid level in the translucent case of Panasonic battery.
Here is one on eBay. I put it back on with new battery. Not sure how much value it is.
https://www.ebay.com/itm/09-13-Subaru-Forester-XT-Battery-Cover-Sleeve-Guard-Blanket-Insulator/173156008020?fits=Make%3ASubaru&hash=item2850e70054:gfUAAOSwQqNcP-IW
Here is one on eBay. I put it back on with new battery. Not sure how much value it is.
https://www.ebay.com/itm/09-13-Subaru-Forester-XT-Battery-Cover-Sleeve-Guard-Blanket-Insulator/173156008020?fits=Make%3ASubaru&hash=item2850e70054:gfUAAOSwQqNcP-IW