If there is a battery in the earpiece; is it safe? There is some controversy about the safety of holding a cell phone to one's ear for extended periods; that's why I wanted an ear piece.

Yes it is perfectly safe. The easiest way to identify whether a bluetooth set is malfunctioning or unsafe is - HEAT. Normally batteries which are about to die or devices malfunctioning will heat up quickly when you charge it.

So unless you dont feel abnormal heat.. they are perfectly safe. Try to remove the BT earpiece when not needed. Your ear canal needs natural air flow. Blocking it with a prolonged use of a BT device could heat up the ear canal. That's where the problem starts! :-)

Yes it is safe. The radiation caused by a Bluetooth headset is very minimal compared to a cellphone.