Running the numbers: Power = I^2 x R. With a resistance of 0.022 ohms and 6 amps of load, you get 0.792 watts of power dissipation.
At this point, you consult the datasheet to determine the junction to ambient temperature rise, in terms of degrees/watt. For this part, it's a maximum of 62.5 C/W. Multiply that by the power dissipation we found out above, and you get ~50C.
So, you're looking at about a 50C rise, which puts your part in the 70C range. That's OK.
It's probably fine. The only thing to watch out: at 70C, the current rating is not 8.3A, but 6.7A. So you don't have a lot of headroom.
EDIT: As Brian Dohler correctly points out, you will be PWMing the MOSFET, which causes switching losses and will increase the temp above what I stated here.
So you may need a heatsink. On those little packages, they are meant to be attached to a heavy PCB by a bottom pad (if you flip them over, they're shiny), which will act like a heatsink.
As this pad is often inaccessible, you could consider mounting something to the plastic top of the chip. While the plastic is not a good thermal conductor, it beats nothing, and you don't need a lot of heatsinking in any case.