The S and E models don't have that problem. I've heard some of the later chipsets for the original model also fixed the problem.
From what I've heard, the 360 was original designed with an environmentally-friendly (read: not lead) solder that had never really been used in a major product. The original design already had heat problems and the solder turned out to be easily melted.
From my memory, it wasn't that they melted too easily, rather they developed stress fractures from thermal cycling. Perhaps due to brittleness relative to lead, or perhaps due to thermal incompatibility (expanding or contracting at the wrong rate)
The original model is the one with the memory card slots on the front (and the only one that comes in white). The S came out in ~2010 has an angled, thinner-in-the-middle design, and the E (came out when the Xbox One was announced) looks like a smaller Xbox One with rounded corners.
The problems I mentioned weren't universal, but they were about as close to it as you could be. Maybe you had an S or an original model that was later in its production.
The 360 has a one year general warranty, but the red ring problems were so widespread that Microsoft added a three year warranty for red rings specifically.
From what I've heard, the 360 was original designed with an environmentally-friendly (read: not lead) solder that had never really been used in a major product. The original design already had heat problems and the solder turned out to be easily melted.