I'm a reasonably experienced gun guy, an AR-15 novice BUT I know my physics and unless the AR is different from everything else in the universe, here is how it works.
Strength:
Fluting an existing barrel, makes it lighter and weaker. Removing material from a barrel makes it weaker, period. There is no voodoo magic that makes it possible to make something stronger by removing metal.
With that said, however, it is possible to make a fluted barrel both lighter and stronger than a comparable non-fluted barrel. But you have to start with a larger blank.
The trick to making a tube strong is to have material around the periphery.
I'm pulling these numbers out of my ear to illustrate a point, so work with me.
If you have a 1" barrel and flute it, it is possible for the resulting barrel to be both stronger and lighter than a non fluted 3/4 inch barrel. The idea is that the fluted barrel is geometrically stronger.
Think of it this way. You have a 3 lb steel rod that is 18" long and solid all the way through. Next you have a 3 lb steel tube that is also 18" long. The wall thickness can be whatever is necessary for it to end up at 3lbs.
Which is more rigid. Obviously, the tube is more rigid than the rod, because it has more metal around its periphery.
I hope this makes some sense.
Regarding heating and cooling.
There are 2 forces at work here.
1) Thermal Mass
2) Surface area
Fluting a barrel reduces its thermal mass, so it will heat up faster. A given amount of thermal energy has less metal to heat, so it heats it more. But it increases its surface area, so it will cool off faster also.
The bottom line is that a fluted barrel will heat up faster initially, but will eventually reach a point where it runs cooler than a non fluted barrel. Its increased surface area means it can transfer heat to the air faster than a non fluted barrel.
So . . in summary. If I was concerned about weight, I'd try to get a large diameter fluted barrel. In reality, if we weren't told what we were shooting, we couldn't tell the difference. So I guess the real issue is: do you think it looks cool and is worth the extra $. Either way, you won't get hurt.
I hope this makes sense to all of you. If you want any clarification feel free to write.
Best regards,
Don