Let me rephrase your question slightly to make it clearer what (I think) you are asking.
Suppose we start with a ferromagnetic material above the Curie point and we cool it through the Curie point in the absence of any external influence e.g. no externally applied magnetic field. And suppose we repeat this experiment many times. Will the final state of the material always be the same?
The answer is that without any external field the total magnetic field will be zero. This is because the magnetic domains formed as we pass through the Curie point will be randomly oriented and their total magnetic field will sum to zero. In this I agree with Pieter.
But it is only the total field that is the same. If we watched an individual spin in the material as we cycled it through the Curie point it would not have the same orientation each time. And unless there was some controlling factor, like defects in the solid, the magnetic domains would not be the same each time.
In any system we have random thermal fluctuations, and in the ferromagnetic above the Curie point there will be random thermal fluctuations in the alignment of the dipoles. As we cool towards the Curie temperature these fluctuations will get larger and larger, and at some point magnetic domains will nucleate and start to grow. These give rise to the domains we observe in the material at low temperature. But the nucleation process is random and hence the final pattern of the domains will be random. So while the overall field is always zero after the cooling the microstructure will not be.