I don't think any SS comes close to CS. I would guess a low-Cr martensitic (410) or ferritic would come nearest. Anything containing austenite phase is completely out.
Try Smithell's Metals Reference, ASM Handbook Desk Edition, or googling.
Spot on, the ferritics are the closest that you will find.
Make sure that you look at alloys with enough Cr to have suitable corrosion resistance.
If you really want to improve heat transfer then select a stronger material and make it thinner. This will have much more impact than changing alloys.