Hmm, good question. The problem with answering it is that is the fact that you are asking us to compare apples to oranges.
There are many types of steel: tool steel, stainless, high-carbon, lo-carbon, etc.
There are many finishes: bluing, bead-blasting, rust bluing, etc.
A stainless steel barrel can have a blued finish. A 4140 steel barrel can have a nickel, stainless, or even bead-blasted finish. The really salient point is what the actual metal of the barrel is made of and how the barrel is constructed.
Other things also affect the rate at which a barrel heats up: size, bore diameter, finish, fluting, and others.
Now, if you are asking for a stainless vs. carbon vs. chromoly vs. new-fangled wonder barrel barrels, that is a different question.
Are you trying to choose between two rifles or different barrel types? If so, please let us know and perhaps we can assist you better.
Hope this helps.