Handling heat includes being able to dissipate the heat that is
generated. The advantage of the bull barrel is twofold: better heat
dissipation and greater
resistance to warping from high heat.
But a heavy barrel also adds to accuracy because it is
more rigid. That's why they put a heavy barrrel on the AR you
pictured - not for dissipating heat. That weapon is meant for very
accurate single shots so why would there be any great need to
dissipate heat?
The rigidity inherent in a heavy barrel certainly contributes to
its accuracy, but the need to dissipate heat still exists.
Sustained semi-auto fire,
such as is encountered in some stages of "Hipower" shooting
competitions, still generates a fair amount of heat (though nowhere
that from full-auto discharges!). It takes only a miniscule amount
of heat-induced warping to make a competition bull barrel lose its
shot-to-shot consistency and accuracy. This may cause target
groupings to migrate by only fractions of an inch at 200 yards, but
HP competitions have been won and lost by just these amounts.
And you mentioned that the barrel in that picture is
made of stainless steel, that's exactly what I meant when I say
that barrels intended for sniping are made with different materials
and methods too expensive for military models.
Those stainless AR bull barrels are made almost entirely for the
civilian market; there is no AR military equivalent.
Current US military specifications for AR barrels call for the
chrome lining of the chambers and bores for enhanced barrel life
under full-auto fire. Chrome-lined barrels are actually
more expensive to
manufacture than the non-chrome-lined barrels found on most
civilian ARs (the exception being Bushmaster, whose non-stainless
barrels are ALL chrome-lined).
The flutes cut into a heavy barrel is to reduce weight -
not to increase surface area for dissipating heat as you claim. And
flutes also help add to the rigidity of the barrel.
It does both. Read the paragraph describing the purpose of
fluting at the bottom of this
page at the Bushmaster website.
Interesting discussion! 
MG