Ok...my take on it.
Weight - obviously carrying around.
Heavy barrels you can send more rounds down before the heat effects POI (point of impact), not to be confused with "take longer to heat up".
I believe they heat up just as quick but hold the heat longer, but you just dont feel it from the outside, due to there being more steel for the heat to transmit through.
By the time a heavy barrel is too hot to touch on the outside, imagine how hot the end of chamber is on the inside...
I can also measure the difference in the cases i fire from sporter to heavy barrels measuring the fired cases...
If i measure the case head to shoulder length, the diameter at the shoulder etc of 5 warm to hot loaded cases fired one after the other from a cold barrel, all cases from a heavy barrel are basically the same size.
However the ones out of the sporter barrel start to get larger dimensions at the 3rd or 4th case..
This to me indicates the point at which thermal expansion begins to change things.
It also correlates with some manufacturors warrantee's--3 shot moa for sporter/5 shot moa for heavy barrel.
Those heavy barrels i imagine have less movement (harmonics) when fired due to their weight--or more technically, their mass. (Ie:its easier to move a 2m long average gauge steel fence post by hitting it with a hammer than a 2m long section of railway iron by hitting with the same hammer).
When i shoot my varmint barrel 22-250 in summer (say 35 degrees) it takes 20 mins to cool down with a damp rag out of the car fridge to suck the heat oit of the barrel.
It only takes half the time or less to cool down the sporter because there is less heat to tranfers to atmosphere.
So in summary, my belief at this point in my experience is that the inside of the barrel (lets face it--the important bit) heats up at the same rate in either a sporter or heavy or bull brl--ie;5 shots of any given cartridge generates a given amount of heat energy-period.
The heat is directly related to barrel erosion.
Sporter barrel will allow heat to transfer away quicker, however will suffer from thermal exansion (POI shift) quicker (due to not having as much 'non-heat effected/thermally stable steel around it).
Thats some of my perspective on them...ill come back later, but gotta go now...
Hope that helps
The man who knows everything, doesnt really know everything...he's just stopped learning...