Oh yeah, the coils will heat right up no doubt. Inherently, 3" coils don't have the surface area to dissipate the heat that will build up properly. Unless it was super long, like an unseen WH coil lol. The coils on those drivers aren't too shabby, but they are far from great.
Even if you are not clipping at all, no matter what frequency, even if it is an extended amount of time playing that is spot on with your vehicle's peak frequency kind of music, where the woofers are physically moving the least, the coils will get hawt. In this case, it is because a 3" coil cannot thermally handle 3kW. But to be honest, these woofers will be most efficient while receiving around 1.5-1.7kW I'd assume, and they will get loud off that. So if possible while tuning your system, try to aim for amplifier settings where you are obtaining 8kW or so; or, utilize the coil configuration to your advantage while wiring up the woofers to the amplifier in order to receive the amount of rated power at a certain impedance on the amplifier, of around 8kW or so. But if competing, hell, go right ahead and wire down and give full power if you are doing a burp! Giving each driver 3kW on a burp wouldn't harm them.
Either way though, 12kW on these quartet of woofers is going to be too much for them in a daily application. But don't let that turn you away, these drivers will get loud off of less power than 3kW a piece, so it's just not needed. And, that isn't a bad thing necessarily.