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Advances in experimental and theoretical methods have dramatically broadened and accelerated research in thermal sciences in the past decade.Our field also has many examples of compelling scientific accomplishments: advances in understanding of thermal transport in nanostructures,the conductance of various types of interfaces,and effects of non-equilibrium between different populations of heat carriers to name just a few.Going forward,I argue that our field will benefit from clear statements of far-reaching "problems" that have the potential to produce breakthroughs in thermal science or technology.I propose two categories of such problems: i)the development of materials with extremely low thermal conductivity or extremely high thermal conductivity subjected to constraints; and ii)enhanced functionality of thermal transport,i.e.,materials with abrupt changes in conductivity,materials with properties that can be modulated,or novel physics that enables new function such as the writing of magnetic information.I will give two examples of science that is motivated by these problems.Low-dimensional quantum magnets based on copper oxides demonstrate that electrons and phonons are not the only significant carriers of heat in materials; near room temperature,the magnon thermal conductivity is comparable to the electronic thermal conductivities of metal alloys.We extract the effective strength of magnon-phonon coupling from time-domain thermoreflectance data using a two temperature model.In metallic multilayers,ultrafast spin currents can be generated using fast temperature excursions and strong temperature gradients.Thermally-driven demagnetization of ferromagnetic layer produces a transient spin current and heat current passing through a ferromagnetic layer generates a spin current due to the spin-dependent Seebeck effect.