How Can I Get Rid of Unsightly Temple Artery (Yes, It Pulses)?

The temporal artery has many branches and it would be technically difficult to ligate an isolated branch without collaterals causing the pulating appearance to return. In the absence of pain (temporar arteritis) it would be very unusual to find a surgeon who would operate based on this indicatio alone. Sclerotherapy is generally resrved for low flow vessels (veins) and not arteries.

Thank you for the question! Artery cannot be eliminated with sclerotherapy or other treatments reserved specifically for varicose or spider veins. One available option is to use injectable fillers around the artery to minimize its appearance. 
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!