Sadly, the Elite doesn't correct the cause of the RRoD. MS bunged another heatsink on some chips, but they're still failing. The problem is that heatsinks only help if you've got enough cool air flowing into the machine to push the hot air away from the heatsinks. The 360 just doesn't draw enough cool air in to let the heatsinks do their job. There's stories around the web (and a mate of mine who works in GAME confirms) about Elites ('Zephyr' systems) failing in exactly the same way as the Premiums.
D'oh!
The 'real' fix will be when the 'Falcon' revision of the 360 gets released. These use cheaper, cooler, smaller processors (65nm instead of 90nm). Apparently, these should appear towards the end of the year. We'll also start seeing Zephyr-based Premiums over here soon -- basically identical to the Elites (HDMI and all), but white and with the regular small HD.
My 360's been repaired twice ... going to try to keep the thing chugging along until those Falcons get released.