How do powering arduino both barrel jack and lipo battery together? I have arduino mega and Lipo batterry such this and Lipo battery charger 5V USB Boost. I am powering arduino normally from barrel Jack with an 9 Volt adaptor. But if there is power cut occur, I dont want to stop, I want powering arduino with Lipo battery. After power come back, arduino contunie to powering from barrel jack again at the same time battery start to charge. How can I succes this. Do you have any sample circuit?
After Majenko♦ comment, I've tried circuit but there is heating problem occur. More then 70 celsius. Is that normal?
Circuit

Termal Circuit
As is described in this post from the arduino forum, There is a MOSFET switch in series with the USB connector +5V input line.  If the battery booster 5V output is connected to the USB input jack, then it will automatically power the UNO whenever power is disconnected from the barrel jack, and will be automatically disconnected whenever at least 7.0V is available at the barrel jack.
If you are experiencing over-heating problems, then you are probably overheating the linear regulator that steps down the barrel jack voltage to 5V.  You need about 7-7.5V at the barrel jack to overcome the 2-2.5V loss through the linear regulator, but anything higher than about 7.5V will just cause the linear regulator to get hotter.