I'd probably fudge it somewhere between plastic cooler and stainless. It may affect your strike temperature estimation in BS2. Then you can adjust it based on your own observations. How well do you hit your target mash temps based on BS2's target strike temps?
I've never changed mine from plastic cooler and I mash in uninsulated stainless. I've found that my initial mash temp ends up high if I use the BS2 recommended strike temp. So usually heat strike to about 2 degrees less than BS2 recommends.
Makes sense right? Uninsulated stainless should absorb heat more easily than a plastic cooler but retain less heat...hence my fancy sleeping bag insulator during the mash.
I'll have to change the specific heat value in BS2 and see if I come closer.