Pitot tube heating is already automatic on most modern aircrafts, actually. The auto mode is on by default and pilots can manually switch that to off for whatever reason would be required (following usually strict procedures.) The problem is that many aircrafts still in circulation are not modern.
As far as I've read - the older Boeing 737 models may not have an auto mode, but I believe the 737 MAX does, and most recent Boeing models, such as the 787. Most Airbus in circulation do have an auto mode too.
As far as I've understood, the AF447 issue was not that the heaters were not ON, but that the pitots got clogged anyway - which apparently can happen in very severe conditions, due to the quantity of small ice balls that can enter the tubes, so that it can get clogged temporarily. IIRC, in the AF447 case, the pitot eventually got rid of the ice, but that was too late. Airbus did have their pitot modified after this on this model, to limit the possibility of this happening, but I don't believe it was at all due to the pilots having forgotten to switch heaters on.
As to pilots knowing what's happening or not: the problem is that at some point, they do NOT know what is happening, because they realize they can't trust automation/or instruments, but also they are in a situation where they can't trust their own perception of things and their basic flying skills - precisely because a big airliner is pretty different from a small aircraft in terms of sensations, and because, as I said earlier, not being able to trust the plane's automated systems and instruments is in itself a big cognitive dissonnance for modern pilots.
Proper training should help of course, but as I said, training tends to be insufficient these days, and mostly on simulators, which only partially reproduces the physical movements/accelerations, and without the stress factor.