Info on Voltage Limiter Operation

Yes the heating is in shunt with load, that is how a regulator works. Same for series pass, or switching buck regulator. The control elements are referenced to the output via comparator. Very basic control theory. The IVR is thermal, but the control is still hysteretic. The on - off contact is driven, hot opens, cold closes. The system seeks balance. The gauge is thermal, and slow so, filtering is less important.

A modern low cost pwm switching regulator with current limit and high input range is available for about $5. I posted information on that months ago, but can't remember now.

I will not comment on your rms theory.....