New Heart Rate Monitor coming today! I have a question???

I am so excited to be more accurately tracking my calories burned. I am curious about something. Does it also include the calories that would have been burned that hour without exercise? or is it only what you burn ABOVE your BMR? For instance if I would have burned 80 calories that hour if I were sleeping, and it says I burned 350, would it be safe to eat back all 350 calories? I have been weighing everything that goes into my mouth, so I don't want to make errors with the calories I am burning. I have generally only been eating 1/2 or less of my calories burned up til now from exercise. I am also curious to see how much my workouts are REALLY burning.

I know I may be over thinking it, and over complicating, just be kind if I am... :)

Thanks to anyone who might have the answer to this question. I did do a search, but couldn't find anything on this question.