That powersupply board is superseded by this one:
https://www.sparkfun.com/products/13032
It mentions 800 ma max. The board looks pretty much the same, so I expect the thermal properties to be the same also.
Explain what you mean with "proportional to the unregulated input I choose". I don't understand what you mean.
The current going into the device is almost as much as comes out at the output. A tiny amount of current goes through the GND pin of the regulator needed to set the operating voltage. The voltage difference between the input and output determines how much power it must burn away (voltage difference times current = power). So with equal current load, the more input voltage you apply the sooner you reach the thermal limit. I assume that the Sparkfun engineers did their thermal calculations properly and it will hold that 800ma current at the maximum input voltage limit. But you can always ask to be safe. (send email to customer or technical support)
