I have pulsating headaches too. I've had chronic headaches since a car accident in 1978. I have learned that when my head begins to pulsate, I'm either developing a migraine which is usually only on one side of the head. If I can catch it when it starts with something like Ibuprophen and caffeine, it will sometimes go away. If your equilibrium is off, you may have an inner ear problem. And the other reason for my HA is my neck being out of alignment. Sometimes the top vertebrae will shift and lay on a blood vessel in your brain. Only a visit to the chiropractor for an adjustment will relieve that, and it takes a couple of days sometimes even after the treatment for the headache to go away. Most headaches that start in the temple are tension, but tension can also build up in the neck and shoulders. In any case, it sounds like it would be a good idea to see a doctor. Good luck.
Donna