Facial capillaries can be treated
Various techniques are available in the armamentarium of the Board Certified Vein Specialist and choose a physician who has added qualification/board certification from the American Board of Venous and Lymphatic Disease, previoulsy known as Phlebology. Be mindful that they may require several treatments for full efficacy.
Thermavein is thermocoagulation or heat induced clotting of small veins and capillaries. There are also other similar types of treatments including VeinGogh, Veinwave and micro needle radio frequency. All of these work in a similar way but use different types of heat to coagulate the small vessels so that they will then dissolve. You should see someone with experience in this area for your treatment.