Perfectly safe!
Tempdrop only transmits a Bluetooth signal in the first 30 seconds when being turned on and when you remove the device from your body and manually initiate syncing. It uses Bluetooth 4.0 to transmit data, which is a very low energy signal (approximately 1000x less than a cell phone). Syncing is only 1-2 minutes per day.
Tempdrop is powered by a standard coin cell type watch battery while it is being worn and recording.
Finally, Tempdrop is made from medical grade materials and has FCC and CE certifications. There is no Nickle in the metal sensor.