You are right, heat is what burns out a barrel, but the damage is usually done in the throat area and is caused by the heat from burning gases, not so much the speeding bullet further down the barrel. A .22 caliber rifle barrel with 5,000 rounds down the barrel you'll likely be able to actually MEASURE the throat erosion but 3/4 way down the barrel may still have good rifling.
Clearly, I am really talking about barrel life reduction due to normal shooting, not melting a barrel down by shooting it until it's red hot
There's a few ways to combat this throat erosion; burn less powder, burn the same powder in a bigger bore, or otherwise reduce the pressure and hot gases that enter the throat.
As we've pointed out, the .204 burns less powder than comparable calibers (like the .220 Swift or .22-250) and flings that little bullet out and faster speeds. It's the best of both worlds - better performance and better barrel life. (although I bet a .223 barrel would just about shoot forever if a guy were to handload down a little, the .220 swift, 17 Remington, and .22-250 are notoriously hard on barrels at max loadings)
One other thing to note is that the .204 as loaded from the factory uses proprietary powders not available to the public that (they say) decrease fouling and increases speed.
Incidentally, I give ZERO credance to worries of barrel life. Even my .22-250 (which I never shoot anymore because of my .204) is said to have a barrel life of "only" a few thousand rounds if loaded hot. Then what happens? The bullet just drops out the end of the barrel and the rifle no longer goes bang? Well no, the bullet still goes where I was aiming, just not with the same benchrest precision it had 3,000 rounds ago. I bet that for most of my varmint hunting and target practice applications my .22-250 will still be shooting well at 4,000 rounds, not the 2,000 round count they say is the end.
And do the math on that: Even if I were to shoot a box of ammo every other weekend all year long, it will take me nearly 8 years to burn out that barrel!
--Duck911