Magnetic material demagnetization through Curie temperature
If this same material is heated beyond Curie temperature and cooled down then this material is demagnetized and put into H=0 &amp; B=0 state, right?


Not quite. As the material cools through its Curie point, it will retain whatever external field is applied at that time. If that field is zero, then it will not be magnetized.


  And from there, the quiescent point follows initial magnetization curve as external magnetic field is applied to magnetize the given material, right?


Given the caveat described above, yes, that's right.



To be more precise, the Curie point is the temperature at which a material switches from being ferromagnetic to paramagnetic. This effect can be useful even if the the material is not ever "permanently" magnetized. For example, there are at least two methods of controlling the temperature of a soldering iron using this.

The "Welller method" uses tips that have a calibrated Curie temperature (to change the temperature, you change tips). There is a magnet in the handpiece that is attracted to the tip when it is below the temperature, closing the switch that applies power to the heating element. When the tip reaches the Curie temperature, a spring pulls the magnet back and opens the switch.

The "Metcal method" uses tips that have a copper core that is plated with a material with a calibrated Curie temperature. The tip is heated by induction from a high-power RF oscillator. When the tip is cold, the "skin effect" forces most of the induced current to flow through the relatively high-resistance plating, heating the tip. However, once the Curie temperature is reached, the skin effect is dramatically reduced, allowing most of the current to flow in the copper and reducing the heat to negligible levels.