Power dissipated by the MOSFET when turned full on is:
Power = Voltage x Current
Voltage = Current x Resistance, subsitute into the power equation:
Power = (Current x Resistance) x Current
commonly written as P=I^2*R
So you want 3 amps of current, you have Rds of 0.2 ohm, Power = 3 x 3 x 0.2 = 1.8W
Find a part with lower Rds and the MOSFET will dissipate less power:
3x3x0.1 = 0.9W
3x3x0.05 = 0.5W
3x3x0.028 = 0.25W, will be nice & cool
Put a 150 ohm resistor between your arduino output pin and the mosfet gate, will keep the arduino pin from being damaged.
Add a 10K pulldown resistor from the gate to ground to ensure the mosfet stays off while the ardiuno is power up, and the arduino pins are not yet driven low by the sketch.