Using Bluetooth Grove on Arduino Mega

Heyho I just recently started working with an arduino Mega 2560. I also want to establish a bluetooth connection between the Grove Module I got and my Android phone with an app from app inventor. Furthermore I want to recieve the Temperature sensor data from the arduino on my phone.

Can you maybe explain how you managed to get things working?

I can see the sensor Data in the Serial Monitor but it somehow wont transmit it to my phone....