The proposed will be a revision of a classic text on heat conduction which is considered to have the most comprehensive coverage with emphasis on the mathematics and underlying physics. The current text has considerable depth and analytical rigor but after the initial introduction and set-up of the given solution scheme, the treatment is usually reduced to a "generic" solution approach. Comments about the physics of the solution (e.g. transient vs. steady-state components and conservation of energy) are not always given. The second half of the current edition is largely dedicated to approximate and numerical schemes. While these are important topics, rigorous coverage is simply not practical in a single conduction course. At the same time an increasingly important topic in thermal science is coverage of micro- and nano-scale heat transfer. The proposed new edition will then lower the emphasis on numerical methods while increasing coverage of key new topics of micro- and nano-scale heat transfer. New examples, problems, and cases will be added and a solutions manual will be available.