Heat and thermodynamics are traditionally taught in the introductory physics course from a predominantly macroscopic point of view. However, it is advantageous to adopt a more modern approach that systematically builds on students' knowledge of the atomic structure of matter and of elementary mechanics. By focusing on the essential physics without requiring more than elementary classical mechanics, this approach can be made sufficiently simple to be readily teachable during five or six weeks of an ordinary calculus-based introductory physics course. This approach can be highly unified, using atomic considerations to infer the properties of macroscopic systems while also enabling thermodynamic analyses independent of specific atomic models. Furthermore, this integrated point of view provides a deeper physical understanding of basic concepts (such as internal energy, heat, entropy, and absolute temperature) and of important phenomena (such as equilibrium, fluctuations, and irreversibility).