Abstract: Low-dimensional materials, such as 2D monolayers, 1D nanowires, and 0D quantum dots and molecules, are rich with many-body quantum phenomena. The reduced dimensionality, strong interactions, and topological effects lead to new emergent degrees of freedom of fundamental interest and promise for future applications, such as energy-efficient computation and quantum information. Thermal transport, which is sensitive to all energy-carrying degrees of freedom and their interactions, provides a discriminating probe to identify these emergent excitations. However, thermal measurement in low dimensions is dominated by lattice contributions, requiring an approach to isolate the electronic thermal conductance. In this talk, I will discuss how the measurement of nonlocal voltage fluctuations in a multiterminal device can reveal the electronic heat transported across a mesoscopic, low-dimensional bridge. We use 2D graphene as an electronic noise thermometer, demonstrating quantitative electronic thermal conductance measurement over a wide temperature range in an array of dimensionalities: 2D graphene, 1D nanotubes, 0D localized electron chains, and 3D, microscale bulk materials. I will discuss ongoing work revealing electron hydrodynamics, interaction-mediated plasmon hopping, spin waves in a magnetic insulator, and an electron-phonon crossover in a bulk spin liquid candidate material.