Heat is one of the most fundamental and ancient environmental stresses, and response mechanisms are found in prokaryotes and shared among most eukaryotes. In the budding yeast Saccharomyces cerevisiae, the heat stress response involves coordinated changes at all biological levels, from gene expression to protein and metabolite abundances, and to temporary adjustments in physiology. Due to its integrative multi-level-multi-scale nature, heat adaptation constitutes a complex dynamic process, which has forced most experimental and modeling analyses in the past to focus on just one or a few of its aspects. Here we review the basic components of the heat stress response in yeast and outline what has been done, and what needs to be done, to merge the available information into computational structures that permit comprehensive diagnostics, interrogation, and interpretation. We illustrate the process in particular with the coordination of two metabolic responses, namely the dramatic accumulation of the protective disaccharide trehalose and the substantial change in the profile of sphingolipids, which in turn affect gene expression. The proposed methods primarily use differential equations in the canonical modeling framework of Biochemical Systems Theory (BST), which permits the relatively easy construction of coarse, initial models even in systems that are incompletely characterized.