I use a Mega 2560 board with a 12V supply. After running for a couple months, it gets a little warm. The 12 to 5V regulator, 7805 clone, heats it.
For those who do not know it yet, there are switching mode regulators which can be used here. There are plenty of suitable types, one example is Recom R-785.0-0.5, in Digikey it is in Product Index > Power Supplies - Board Mount > DC DC Converters >.
By the way, I have not replaced the regulator yet, "I'll do it any day now". There may be voltages coming from the wrong direction to the regulator. I mean, supply voltage from the USB when there are no 12V supply. I think it is best to try to protect the regulator with diodes.
All this means, you should be familiar with electronics to try this now.