Yup, you'd need a new mattress.  I use the aircore mat Big Agnes sells to use with the bag.  

Big plus:  There's no foam inside the mattress so it packs incredibly small.

Big minus:  There's no foam inside the mattress so it takes longer to inflate and deflate.

No effect:  There's no foam inside the mattress which seems to have no bearing on the insulative properties of the mattress.

I think it's like 2 or 2.5" thick when inflated.  Mighty comfy, whatever it is.