Even at fairly low current using power supplies greater than 9V can result in the voltage regulator failing in time...

I did some testing with different power supplies rated between 7 and 20 volts and a fixed load of 0.25 mA (a 4 by 20 LCD)...

20 volt supply: 3.75 Watts @ 250mA

15 volt supply: 2.5 Watts @ 250mA

12 volts supply: 1.75 Watts @ 250mA

9.0 volts supply: 1 Watt @ 250mA

7.1 volts supply: 0.525 Watt @ 250mA

To be on the safe side connect up your power supply and measure the current drawn by the board...

Multiply the current time the voltage drop across the regulator (the supply voltage - 5 volts) to see how much heat is being dissipated...

It appears given a proper heatsink, a maximum rating of 7 watts can be achieved (but for how long?)

IMHO, it will fry long before you reach these levels... I suggest you keep it below 1 Watt and use a 7 or 9 volt power supply...

If you draw less current you can probably use a 12 volt supply but if using 20 volts, I hope the current is less than 60mA...

The device is probably capable of dissipating a lot more but why take the chance...

I used 12 volts with a load of 0.25mA for 5 minutes and could smell the heat... I almost burned my finger too...