Whats the best way to keep an Arduino in a waterproof junction box and prevent overheating?
The linear regulator on an Arduino works by converting excess voltage to heat. If you power it with 12V and draw a full amp from it it will turn (12-5)*1a or 7 watts of power to heat, and quickly overheat even if it's not in a box.
If you power it from 6.5V and only draw 300mA from it, it will turn (6.5-5)*.3, or a little under half-a-watt. While the Arduino is idling it will probably only draw 50mA, so less than 1/10th of a watt of heat.
For infrequent, short bursts of a few seconds you can probably get away with drawing 500mA of power without overheating.
Or skip the internal regulator and use a buck style voltage regulator. Those generate a LOT less heat.
Edit:
For a project I did recently, I used an external 5V regulated supply for everything. I cut a USB cable and soldered the red and black (+5V and ground) to the 5V supply, and plugged that into the Arudino's USB connector. That feeds 5V into the Arduino.