It is true that all foams will soften with use, especially when new. What you’re experiencing is quite normal, as the edges and the center of the mattress aren’t used as much and those areas are still “like new” as compared to the areas where you’ve concentrated your sleep activity.
As for a warranty claim, Tempurpedic allows up to .75" of visible body impression (when placed upon a proper foundation - make sure that yours is appropriate and properly supported) before considering there to be a defect in the foam. The softening in the area where the mattress is used is not generally considered a defect.
It sounds as if you sleep prone, and if that is the case generally something using visco-elastic foam can often allow too much sinking and could be contraindicated for such a posture, as generally something that offers a bit of a “harder” surface comfort would be preferred. Sleeping prone places your lumbar/lower thoracic region in a very weak posture, and accentuating the lordotic curvature of the low back by sinking in too deeply into the comfort materials of a mattress can result in waking up with a sore back, which you unfortunately seem to be experiencing.
I can’t offer you any sort of advice regarding your current mattress, as it seems that it isn’t defective, but in fact simply a comfort that isn’t appropriate for your sleeping style, level of flexibility, comfort preference, core strength, and so on. And comfort isn’t something that is considered a manufacturing defect.
If you are considering a new mattress, you may find this article interesting about different sleeping postures. Generally, a prone sleeping needs something that has a bit of a harder surface comfort with good deep support. There are many combinations of materials that can provide such a level of comfort and support, but you’d need to make sure that whatever you select uses food quality and durable materials, There are some really detailed guidelines for selecting a mattress in the shopping guidelines here on the forum.
I hope that helps you out.
Jeff Scheuer, The Beducator
Beducation / Mattress To Go