xvii, 189 p. ： ill. (some col.) / Low-dimensional electronic systems, systems that are restricted to single energy levels in at least one of the three spatial dimensions, have attracted considerable interest in the field of thermoelectric materials. At these scales, the ability to manipulate electronic energy levels offers a great deal of control over a device's thermopower, that is, its ability to generate a voltage due to a thermal gradient. In addition, low-dimensional devices offer increased control over phononic heat flow. Mesoscale geometry can also have a large impact on both electron and phonon dynamics. Effects such as ballistic transport in a two-dimensional electron gas structure can lead to the enhancement or attenuation of electron transmission probabilities in multi-terminal junctions. The first half of this dissertation investigates the transverse thermoelectric properties of a four-terminal ballistic junction containing a central symmetry-breaking scatterer. It is believed that the combined symmetry of the scatterer and junction is the key component to understanding non-linear and thermoelectric transport in these junctions. To this end, experimental investigations on this type of junction were carried out to demonstrate its ability to generate a transverse thermovoltage. To aid in interpreting the results, a multi-terminal scattering-matrix theory was developed that relates the junction's non-linear electronic properties to its thermoelectric properties. The possibility of a transverse thermoelectric device also motivated the first derivation of the transverse thermoelectric efficiency. This second half of this dissertation focuses on heat flow phenomena in InAs/InP heterostructure nanowires. In thermoelectric research, a phononic heat flow between thermal reservoirs is considered parasitic due to its minimal contribution to the electrical output. Recent experiments involving heterostructure nanowires have shown an unexpectedly large heat flow, which is attributed in this dissertation to an interplay between electron-phonon interaction and phononic heat flow. Using finite element modeling, the recent experimental findings have provided a means to probe the electron-phonon interaction in InAs nanowires. In the end, it is found that electron-phonon interaction is an important component in understanding heat flow at the nanoscale. This dissertation includes previously unpublished co-authored material. / Committee in charge: Dr. Richard Taylor， Chair； Dr. Heiner Linke， Advisor； Dr. David Cohen， Member； Dr. John Toner， Member； Dr. David Johnson， Outside Member