Which current should I use to determine the Watt?
Your guess that "it will be limited to 3.16A" is not the full story because you are trying to draw more current from the power supply than it can deliver. 

There are a few scenarios for how over current will be handled depending on the power supply you're using (I'm assuming a standard CV -continuous Voltage- power supply):


Power supply with Constant Current (CC) Limit: The current supplied will be ~3.16A but the voltage will drop to 3.16A x 3Ohms = 9.48V (for you 3 Ohm example), reducing the power accordingly .


The Power supply will Fault because of over-current, setting the output voltage to zero whilst the over-current condition persists.
The power supply does not have any over-current protection  and will try to supply the power needed, but this causes lower output voltage, higher ripple voltage, possible over heating of the power supply components and eventual failure.