Am I correct thinking a fluted barrel will be slower to get hot and will be stiffer then a regular barrel?
No, this thinking is not correct.
Heating up happens fast enough, it’s really simply a function of mass (heat transmittance within the steel). The fluted barrel will heat up effectively just as fast as a non-fluted barrel of the same weight. If you want a barrel to heat up slower, build a heavier barrel.
Cooling, however, is a function of surface area (transfer of heat between the steel and air around it). The increase in surface area by fluting - as compared to either a barrel of the same diameter but heavier weight, or a barrel of the same weight but smaller diameter - is very small, especially for smaller diameter barrels with relatively shallow fluting.
Weight reduction can be another advantage for fluting a barrel, say, in the combination of a sporting rifle with a suppressor, such a sufficient shoulder is required, but overall rifle weight is an extreme concern (adding a pound or more out front). This is challenging, as not much shoulder is needed on a sporting barrel, so the fluting can’t be terribly deep - limiting the amount of weight to be reduced by fluting rather than simply using a lighter contour.
Stiffness per weight can be a significant contribution from fluting, but again, in smaller diameter barrels with shallow fluting, this is minimal at best, as the relative diameter change is near zero.
The risk, of course, in introducing asymmetrical stress in the barrel by fluting is significant as well. If a barrel is cryogenically relieved post fluting, this can be resolved. Deeply fluted, large diameter barrels can 1) increase cooling surface area, 2) reduce weight, and 3) increase stiffness:weight ratio, but these deeper fluting cuts run the greatest risk of inducing asymmetric stresses.
But it’s hard to deny how sexy fluted barrels really can be.
