We extend the thermodynamic approach for the description of the thermal Hall effect in two-dimensional superconductors above the critical temperature, where fluctuation Cooper pairs contribute to the conductivity, as well as in disordered normal metals where the particle-particle channel is important. We express the Hall heat conductivity in terms of the product of temperature derivatives of the chemical potential and of the magnetization of the system. Based on this general expression, we derive the analytical formalism that qualitatively reproduces the superlinear increase of the thermal Hall conductivity with the decrease of temperature observed in a large variety of experimentally studied systems [Grissonnanche et al., Nature (London) 571, 376 (2019)NATUAS0028-083610.1038/s41586-019-1375-0]. We also predict a nonmonotonic behavior of the thermal Hall conductivity in the regime of quantum fluctuations, in the vicinity of the second critical field and at very low temperatures.
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