Looks like the heatsink on that board would be good for about 2W without a fan.
Yeah - they always put dinky heat-sinks on those things, don't they (crazy thing is, I've never been able to find those heat-sinks sold separately, nor an aluminium extrusion profile that would work, either)?
The L298 can also be configured in a bridged mode to give you 4A of current output into a single motor (you're gunna need a bigger boat - I mean heatsink).
That said - without knowing the stall current rating of the motor - all this speculation is moot point.
I have some of those motors, but I don't recall what I measured the current as.
Best thing for the OP to do is to carefully remove the motor from the gearbox (IIRC, this can be done with a little work), then measure the resistance of the windings via the motor terminals; rotating the motor a bit (take multiple readings, then average them). Then use Ohm's law @ 12 VDC which will give you a close value to the stall current of the motor.
I used to recommend the "clamp the shaft, apply voltage and measure current" method, but after learning (and reading more) on the above method (valid only for DC motors, btw) - it is much safer (especially for large torque/powerful motors) and generally easier to do. Plus you won't burn out a power supply, strip gears, or have other nastiness occurring.