Is it permissible to undergo a Thermage procedure to tighten body sagging, knowing that it may necessitate revealing the 'awrah (intimate parts), and does psychological necessity permit that?

There is no impediment to performing a skin-tightening operation to remove excess sagging that has become a repulsive blemish. That which is done to remove a defect is permissible (halal). It should be performed by a female doctor if possible, and it is permissible to expose the 'awrah (intimate parts) out of necessity.