As it is customarily stated in textbooks, taken alone, the so-called "zeroth law of thermodynamics" fails to deliver this information, but the statement of the zeroth law of thermodynamics by James Serrin in 1977, though rather mathematically abstract, is more informative for thermometry: "Zeroth Law – There exists a topological line which serves as a coordinate manifold of material behaviour. The points of the manifold are called 'hotness levels', and is called the 'universal hotness manifold'."Serrin, J. (1978). The concepts of thermodynamics, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations. Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977, edited by G.M. de La Penha, L.A.J. Medeiros, North-Holland, Amsterdam, , pages 411-451. To this information there needs to be added a sense of greater hotness; this sense can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of thermal radiation is proportional, by a universal constant, to the frequency of the maximum of its frequency spectrum; this frequency is always positive, but can have values that tend to zero. Another way of identifying hotter as opposed to colder conditions is supplied by Planck's principle, that when a process of isochoric adiabatic work is the sole means of change of internal energy of a closed system, the final state of the system is never colder than the initial state; except for phase changes with latent heat, it is hotter than the initial state.Planck, M. (1926). Über die Begründung des zweiten Hauptsatzes der Thermodynamik, S.-B. Preuß. Akad. Wiss. phys. math. Kl.: 453–463.Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, London, pp. 42–43.
As it is customarily stated in textbooks taken alone the so-called "zeroth law of thermodynamics" fails to deliver this information but the statement of the zeroth law of thermodynamics by James Serrin in 1977 though rather mathematically abstract is more informative for thermometry "Zeroth Law – There exists a topological line which serves as a coordinate manifold of material behaviour The points of the manifold are called 'hotness levels' and is called the 'universal hotness manifold'"Serrin J (1978) The concepts of thermodynamics in Contemporary Developments in Continuum Mechanics and Partial Differential Equations Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations Rio de Janeiro August 1977 edited by GM de La Penha LAJ Medeiros North-Holland Amsterdam  pages 411-451 To this information there needs to be added a sense of greater hotness; this sense can be had independently of calorimetry of thermodynamics and of properties of particular materials from Wien's displacement law of thermal radiation the temperature of a bath of thermal radiation is proportional by a universal constant to the frequency of the maximum of its frequency spectrum; this frequency is always positive but can have values that tend to zero Another way of identifying hotter as opposed to colder conditions is supplied by Planck's principle that when a process of isochoric adiabatic work is the sole means of change of internal energy of a closed system the final state of the system is never colder than the initial state; except for phase changes with latent heat it is hotter than the initial statePlanck M (1926) Über die Begründung des zweiten Hauptsatzes der Thermodynamik S-B Preuß Akad Wiss phys math Kl 453–463Buchdahl HA (1966) The Concepts of Classical Thermodynamics Cambridge University Press London pp 42–43