You "feel" that it is close huh ? Is it the same way one "feels" which feeler gauge fits a gap ?
If you go to matweb.com and type in 416 into the search window and then look at the properties of some drawn / rolled steel (which is what barrels are) and then compared to a chrome moly you might be surprised.
Example:
MatWeb - The Online Materials Information Resource
416 Stainless Steel, tempered and cold drawn bar 25 mm diameter
24.9 W/m-K @100C and 28.7 W/m-K @500C
An alternative 4140 CM (which is what Lilja uses for its CM barrels)
MatWeb - The Online Materials Information Resource
AISI 4140 Steel, normalized at 870°C (1600°F), air cooled, 25 mm (1 in.) round
42.6 W/m-K @100C and 33.0 W/m-K @600C
So lets see: 42.6/24.9 = 1.71x the thermal conductivity. An increase of 71%. Now a politician might tell you that's not much, but to anyone who cares about science a 71% difference is huge. The difference at 500C hardly matters since the barrel would probably have set your stock on fire already. But 100C is way past the point we should ever let a barrel get to in the first place.
Chrome moly steel is considerably stronger than stainless steel which is why it is the material of choice for critical fasteners and the like. 400 series stainless steels resist atmospheric corrosion and are better suited to exposure to humidity, condensation and the like, although they are certainly not rust free. 300 series stainless steel are considerably more rust resistant, but have even poorer mechanical properties than 400 series stainless steel. It has a 50% bigger coefficient of expansion, which alone is a major factor in making it unsuitable for anything that is exposed to strong temperature gradients.
316L, one of the most common "true" stainless steels is listed as having a thermal conductivity of 14.0 - 15.9 W/m-K @0-100C - you will note 1/3 of 4140 CM.
The fact is that the differences in thermal conductivity between 400 and 300 series stainless steel and CM steel is huge. If you have ever had to build anything that has to reliably operate over a large temperature range, you will discover these differences pretty quickly.
Speculation in these forums does not contribute to the improvement of the knowledge base. Now I will admit that I speculated regarding 2 different scenarios, where there could be a reason for choosing the one type of material over the other. That's not really speculating, since the military chooses chrome moly for all of its tactical barrels, sometimes with a chrome plated bore to resist rust given battlefield conditions. The chrome will burn off in the throat, since it is very thin, and it does reduce accuracy too. However, there was no speculation on the material properties at all.
No disrespect westcliff, but i disagree. I feel thermal conductivity it very close between carbon steels and stainless and stainless typically has a much higher melting point and less fatigue at higher temperatures, especially the 300 series.