Thermal and thermoelectric transport measurements in quantum engineered materials platforms can reveal physical behaviors hidden to purely electrical transport. Thermal conductivity measured with Johnson noise thermometry can probe the details of electronic scattering and interactions, and thermopower measurements provide a unique signature of the entropy per particle. These techniques can be applied to study emergent behavior in exotic quantum systems, such as spin waves in 2D magnets, vortex dynamics in superconductors, and topological physics in the quantum Hall regime. Hydrodynamic electron systems, where electron-electron interactions dominate, can show novel transport phenomena such as the breakdown of the Wiedemann-Franz law (a relation between electrical and thermal conductivity obeyed in almost all materials) observed in graphene. Investigating and engineering the thermoelectric properties of quantum materials, such as increasing the thermoelectric figure of merit, also has broad applications for the development of nanoelectronic devices.