Does it only make the noise when the car is moving?
Any recent repairs in the area you hear the noise?
How many miles on your Toyota?
The pulsating brakes is most likely warped brake rotors. The fact that the noise is louder when it heats up sounds like you have a cracked brake pad. Has anyone actually removed the pads and checked them? Even if there is a lot of material left on the pad, the material can be broken causing a noise.
I recommend replacing the pads and machining the rotors.