There's a great deal of misinformation and confusion about fluted barrels. I'll break it down to a few facts:
1) For any given weight, a fluted barrel will be stiffer than a standard barrel. Due to its greater surface area, it will also dissipate heat better.
2) For a given diameter, fluted barrels will be less stiff, but lighter than their unfluted counterpart.
Some factors tend to negate the positive effects of fluted barrels. First, barrel cooling is nice between strings, but it's not the only factor in the heat dissipation curve. A Heavy barrel might dissipate heat slower, but it absorbs more heat and doesn't get as hot in the first place for a given string of rounds. The Weight (Mass) of a barrel is the most important factor to consider with the majority of shooting situations. A very thick barrel will soak up more energy allowing you to shoot more rounds in a short period of time before the barrel gets too hot.
Another factor to consider is bore temperature. When you are speaking accuracy, you speak about barrel temperature, but bore temperature is critical to the life of a firearm. The reason most MG barrels aren't fluted is because it takes MASS to soak up all of the heat that's being generated on the surface of the bore. There would only be a slight advantage for an air-cooled MG to allow the barrel to cool down quicker. This advantage doesn't really justify the extra cost associated.
The final factor I'll illustrate is the airspace factor. A radically fluted surface such as a car radiator will only transfer heat to the air if there is sufficient air flowing over the cooling surfaces. The difference in heat transfer on a weapon (which usually has less than 10mph air flow over its surface) with or without flutes is nominal and tends to negate many of the theoretical benefits of fluting. Couple that with handguards which block the wind and your looking at, WAG here, about a 5% increase in cooling per weight with about a 10-20% decrease in the time it will take the barrel to heat up due to its reduced mass.
Where the Fluting comes into its own is if you have the money to spend and want a lighter barrel. The acid test for me... I bought a heavy-profile barrel. I'm a firm believer that barrel mass is the most important factor in cooling. Handling is subjective, but I like the way my RRA heavy profile barrel handles. Accuracy? I don't see as that is as much a factor of profile over the quality of the barrel.