The growing technical and social interest in energy has made the study of thermal properties more relevant and exciting in recent years. A group of the world's leading experts on this subject gathered April 27-May 1, 2014, at Purdue University (West Lafayette, IN, USA) for the 32nd International Thermal Conductivity Conference and the 20th International Thermal Expansion Symposium. This event has a long and storied history of innovation, and this meeting's proceedings carried on this great tradition. This community shares a sense of global motivation and collaboration. These proceedings represent new results from leading laboratories and researchers on topics including composites/granular media, thermal insulation, modeling, steady and transient measurements, and thermal expansion. The materials of interest span across scales from nanometers to meters, bringing together ideas and results from across the length spectrum. Similarly, measurement techniques range from ultra-short timescales to steady state. Such technical diversity creates a unique and rich blend of ideas and physical principles that the reader will find interesting and illuminating.