In the picture below of the potential of the Higgs field, we can see that the field has its highest energy if the field is zero, i.e. if no Higgs particles are present.
The symmetry is restored at an extremely high temperature, leaving us with a Higgs field that is zero everywhere, i.e. no Higgs particles are present at that high energy.
I can't imagine how the Higgs field "knows" that the temperature is so high that the Higgs field evaporates. Of course, heat is transferred to the Higgs field but how can the field "sense" this high temperature. Are the energies involved in the collisions of particle fields with the Higgs field high enough to let the broken symmetry evolve into the non-broken symmetry?
For almost all phase transitions (like the one to a superconducting state, to a Bose-Einstein condensate, the ones involving solid-liquid-gas or the ones here, except the ones involving SSB) I can see how they relate to temperature. But not for this one.
So, what's going on in the transition from the presence of the Higgs field to the non-presence (evaporation)when the temperature is high enough? And what stuff is the "carrier" of this temperature? The Higgs field itself?