<p>Buildings consumed 32% global energy and emitted 34% CO₂ in 2023, while indoor air pollution caused over 3.2 million premature deaths in 2020. Creating low-carbon and healthy buildings is of great significance to sustainable development. Traditional thermology, consisting of engineering thermodynamics and heat and mass transfer, is based upon reductionism and cannot identify the minimum carbon emission process from infinite possible processes. To overcome these limitations, this study proposes an analytical framework, named as <i>analytical building thermology</i>. It differs from traditional thermology in three aspects: (1) it is based upon holism rather than reductionism; (2) it is based upon the least action principle rather than the second law of thermodynamics, enabling its application to non-equilibrium systems with multiple coupled variables (such as temperature, humidity, pollutant concentrations) which is beyond the scope of the traditional engineering thermodynamics; (3) it employs an inverse-problem and functional analysis (mapping from functions to number field) instead of the traditional forward-problem and function analysis (mapping from number field to number field). The analytical building thermology is demonstrated through three case studies: (1) proving that the Otto, Diesel, Brayton, and Rankine cycles are all the maximum-efficiency cycles under given constraints without invoking the second law; (2) deriving ideal variable thermal physical property functions for building walls that respond with local climate changes; (3) determining the ideal mass-work cycle and the COP of a salt solution cycle with infinite or finite heat and mass transfer areas: 41.4 and 4.09, respectively. The results confirm that analytical building thermology can address heat-mass-work conversion and transfer processes, providing a systematic pathway to maximal potentials of future low-carbon, healthy, and intelligent buildings.</p>