Shouldn't Tying off Only the Superficial Branch of the Temporal Artery Be Successful?

This is a question for your Vascular surgeon and neurosurgeon.  Rarely do arteries bulge on the skin.  Most are well hidden under tissue.  Proceed with caution.

Thank you for the question! It is rather difficult to fully assess your situation without an in-person exam. Such an exam would be necessary to ensure that your bulging vein is not an artery. An artery cannot be eliminated with sclerotherapy or other cosmetic treatments reserved specifically for varicose or spider veins. One available option is to use injectable fillers around the artery to minimize its appearance. If you are seeking to eliminate an artery, I'd recommend seeing a vascular surgeon. 
An in-person exam with a board-certified plastic surgeon is the best way to assess your needs and obtain expert medical advice. Best of luck!

A thorough examination and history taking is necessary. If there is temporal arteritis, an excisional biopsy may be necessary. Cosmetic temporal artery surgery is rarely done. 

Greetings to you in Bangor~

Rather than try to remove the vessel that you find bothersome, another option would be to disguise it with something lie Radiesse or Sculptra.  These fillers and volumizing agents can thicken the tissue in the area surrounding the vessel and make it much less noticeable without having to compromise any of the vascular supply to the area. Something to consider.

Good luck~

Dr. Grant Stevens      Marina del Rey, CA        Marina Plastic Surgery       The Institute         310.827.2653

The image you show here is not of an artery, rather this is a vein.  If you are considering cosmetic improvement of this vein, just one option here is viable and it is sclerotherapy. A phlebectomy could also be possible but not recommended.  Even sclerotherapy will carry some significant risks.