Barrel Heat: Stainless or Carbon?

I don't think there is any difference is regards to handling heat.

I thought stainless was more resistant to erosion caused by heat (?)

I did a bit of googling and came up with some figures for heat transfer of various steels based on BTU/ ft hr. carbon steel is 45, carbon moly - 43, chrome- moly steel ranges from 28 to 42 depending on it's composition. 3. # class SS is only 16 and I found nothing on 4 class SS but it should be a little better than the 3 class..I don't believe the 3 class true SS is used in firearms because of the machining difficulties but who knows what is possible with newer manufacturing processes of today. Based on this the carbon steel barrel should transfer heat much better than the SS barrel but then you have to factor in the better corrosion properties of SS. What this amounts to is I'm not a metallutgist so take my post with a grain of salt. If I, personally, were choosing a barrel to stand up to the heat of rapid fire I would go with SS based on what experience I have with it in uses that have nothing to do with guns.

Stainless steel bolts are used in thermal isolation joints in buildings because they do not transfer heat/cold as much as carbon steel bolts.