Cauterization is a technique that dermatologists have been using for decades. A very fine electric needle is used that chars and hence destroys anything it touches.
It is generally used to eliminate small benign growths such as benign keratoses, tiny red growths called cherry angiomas, and spider veins on the face.
Spider veins on the legs and elsewhere on the body do not respond to cautery; lasers or sclerotherapy are used to eliminate veins in these locations.
Cauterization at a low setting is somewhat uncomfortable, but can usually be performed without the use of local anesthesia. If the growth is deep, local anesthesia is necessary.