Understanding the energy transport properties of hot energy carriers is of great importance for a diverse range of topics from nanoelectronics and photochemistry to the discovery of quantum materials. While much progress has been made in the study of hot carrier dynamics using ultrafast far-field time-resolved spectroscopies, it remains a great challenge to understand hot carrier transport and interaction dynamics at the nanoscale. Existing theoretical models yield only qualitative predictions that are difficult to validate against experiments. Here we present a theoretical framework that extends the study of near-field thermal radiation into the ultrafast time domain, enabling sensitive local probing and quantitative study of nanoscale hot electron and phonon transport effects that have been challenging to quantify. The proposed technique of near-field hot carrier nanoscopy directly links the features of different nonequilibrium effects to near-field thermal absorption and scattering by a scanning nanotip. Our model predicts ultrafast thermal radiation in response to photoexcitation, as well as elucidates the nanoscopic radiation properties of a number of hot carrier dissipation pathways, including nonlinear electron supercollision, second sound, and nonlocal phonon transport. This work is expected to guide experiments to identify the fundamental constraints unlocking thermal wave (second sound) propagation and address the roles of competing hydrodynamic and ballistic phonon effects at the nanoscale.