Is your hr only high like that in the morning? What is it, at rest in the evening before bed?
I have a similar problem. When I wake up in the morning I often feel a little light headed and my heart feels like it's beating very fast, especially when I'm standing. In my case, it seems to be related to dehydration, because it usually goes away 30 minute to an hour after I drink a glass or two of water.
Have you had your electrolyte, magnesium and thyroid levels checked? have you seen a cardiologist?
Could be due to a whole number of things. I don't think it is anything to worry too much about but I would go and get a physical and see if there are any issues that need to be addressed. My biggest concern might by issues with the thyroid so just go and get a check up. Take care. Hope you can get this resolved.