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 571, 376 (2019)]. We also predict a non-monotonic behaviour of the thermal Hall conductivity in the regime of quantum fluctuations, in the vicinity of the second critical field and at very low temperatures. Sign up to receive regular email alerts from Physical Review Letters Enter your email APS Current Issue Earlier Issues News & Announcements About this Journal Journal Staff About the Journals Join APS AUTHORS General Information Submit a Manuscript Publication Rights Open Access SCOAP3 Policies & Practices Tips for Authors Professional Conduct REFEREES General Information Submit a Report Update Your Information Policies & Practices Referee FAQ Guidelines for Referees Outstanding Referees LIBRARIANS General Information Subscriptions Online License Agreement Usage Statistics Your Account STUDENTS Physics PhysicsCentral Student Membership APS MEMBERS Subscriptions Article Packs Membership FAQ APS News Meetings & Events Privacy Policies Contact Information Feedback ISSN 1079-7114 (online), 0031-9007 (print). ©2020 American Physical Society. All rights reserved. Physical Review Letters™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Information about registration may be found here. Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.