  We extend the thermodynamic approach for the description of the thermal Hall
effect in the vicinity of a superconducting phase transition, in the
fluctuation dominated regime. We show that the Hall heat conductivity is
proportional to the product of temperature derivatives of the chemical
potential and of the magnetization of the system. We argue that the latter
derivative shows the strong singularity in the vicinity of the phase
transition, while the former does not contain the characteristic for fermionic
systems smallness (T /EF ), what additionally increases the effect. We derive
the analytical formula predicting the temperature dependence of the thermal
Hall conductivity in the vicinity of the critical temperature for different
magnetic fields. Moreover, we study the phenomenon in the regime of quantum
fluctuations, in the vicinity of the second critical field and at very low
temperatures. We demonstrate how it fades away in a full agreement with the
third law of thermodynamics. The developed approach qualitatively explains the
recently observed giant thermal Hall effect in cuprates [1].
