Most of these older non-low dropout style regulators used a zener clamp diode with an opamp for the adjustable reference. That's where most of the internal hiss is generated.
I was always under the impression that the constant voltage adjustment to regulate the constantly changing incoming voltage generates the audible noise in these regulators.
In a good regulator design you will see around 1 mv of noise, that's a bit more than -60 db down, not bad. ...In as this is for a DC heater design, most of the audio concerns can be eliminated.