Thermage or Blepharoplasty for Sagging Under Eyes?

Dear SR, the device or procedure you choose really depends on what your goals are. Thermage will give some improvement to the lower eyelids- improved texture and tone of the skin, moderate to very good improvement of the upper eyelids and will help elevate the eyebrows if enough pulses are used in the areas.
Eyelid surgery will improve all of the elements- skin, fat bulging, muscle tone and eyelid position- a more complete rejuvenation. Surgery has more downtime but the results will last 5 to 7 years or more.
With Warm Regards,
Trevor M Born MD

Personally, I doubt that Thermage will give you meaningful improvement for lower lid aging. It is the combination of shape and coverage that distinguishes a youthful lower lid region: The transition from cheek to lower lid should be soft and convex, the coverage should be made of smooth skin. If it is only skin that is the concern (which it rarely is), a skin-only blepharoplasty can be entertained. Alternative, skin resurfacing (laser, peel) could be discussed but remember that the treatment has to go deep enough to cause enough skin tightening for fine wrinkles to improve.
Most commonly, volume loss, fat excess and skin wrinkling go hand in hand.
The most important step is the initial analysis of your particular condition. See an experienced facial plastic surgeon for a thorough evaluation which should be followed by a personalized plan.