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Using nanoscale structures, systems have the potential to radically alter the way that we use, and think of heat. It is a field that abounds with opportunity, from expanding the limits of thermal conductivity, to diagnostics, phononics, and adding worth to heat beyond its face caloric value. In this chapter we give a brief survey of recent experimental progress, and a discussion of computational approaches to nanoscale thermal problems. Explored are the merits of calculation (theory) versus simulation. In the second part of the chapter a set of case studies are used to demonstrate a selection of computational methods for simulating and analyzing heat transfer and dissipation in nanoscale systems. Despite much progress in advancing methodology for computing and simulating heat, numerous important challenges are yet to be surmounted. Our aim in this chapter is to encourage and spur much-needed further work in this exciting field.

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