yup, 100% correct on the greater the mass the longer it takes to heat up, but the less the mass the quicker the barrel cools off. so just have to decide what type of shooter you are and how many rounds you will be putting down range in what type of time period.
as for fluting: fluting doesn't make a barrel more rigid, but because fluting cuts weight, you can have a barrel that is more rigid with fluting than a thinner barrel that doesn't have fluting. also, fluting creates more surface area that is exposed to the air so it does increase cooling, but not by much as again mass is the big factor in cooling. so basically fluting is for a person that wants a more rigid barrel but at the same weight as a slightly thinner barrel... or someone that just thinks it looks cool. haha.