Propagation and relaxation of nonequilibrium quasiparticles in superconductors are fundamental for functioning of numerous nanoscale devices, enabling operation of some of them, and limiting the performance of others. The quasiparticles heated above lattice temperature may relax locally via phonon or photon-emission channels, or diffuse over appreciable distances in a nanostructure altering the functionality of their remote components. Tracing quasiparticles experimentally in real-time domain has remained a challenging task owing to their rapid dynamics. With electronic nanothermometry, based on probing of the temperature-dependent switching current of a superconducting nanobridge, we monitor heat pulse carried by a flux of nonequilibrium quasiparticles as it passes by our detector with a noise-equivalent temperature of 10 mK/N, where N is the number of pulses probing the bridge (typically N=10000), and temporal resolution of a single nanosecond. The measurement provides the picture of quasiparticle diffusion in a superconducting aluminum strip and direct determination of the diffusion constant D equal to 100 cm2/s with no energy dependence visible.