In modern microelectronic devices, hot electrons accelerate, scatter, and dissipate energy in nanoscale dimensions. Despite recent progress in nanothermometry, direct real-space mapping of hot-electron energy dissipation is challenging because existing techniques are restricted to probing the lattice rather than the electrons. We realize electronic nanothermometry by measuring local current fluctuations, or shot noise, associated with ultrafast hot-electron kinetic processes (~21 terahertz). Exploiting a scanning and contact-free tungsten tip as a local noise probe, we directly visualize hot-electron distributions before their thermal equilibration with the host gallium arsenide/aluminium gallium arsenide crystal lattice. With nanoconstriction devices, we reveal unexpected nonlocal energy dissipation at room temperature, which is reminiscent of ballistic transport of low-temperature quantum conductors.