This e-book is a compilation of selected papers from the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Finland, July 2004 and is guest edited by Professor Vaughan Voller of the University of Minnesota. The papers in this special issue highlight many of the important active areas in numerical heat transfer research—simulation of multi-physics problems, the refinement of treatments for boundary conditions, the identification of efficient solvers, the development of new approaches, and the extension of numerical heat transfer techniques into other fields. Together they provide a window on the advances made in numerical methods for thermal problems in the last 25 years.