Decay of plasmons to hot carriers has recently attracted considerable interest for fundamental studies and applications in quantum plasmonics. Although plasmon-assisted hot carriers in metals have already enabled remarkable physical and chemical phenomena, much remains to be understood to engineer devices. Here, we present an analysis of the spatio-temporal dynamics of hot electrons in an emblematic plasmonic device, the adiabatic nanofocusing surface-plasmon taper. With femtosecond-resolution measurements, we confirm the extraordinary capability of plasmonic tapers to generate hot carriers by slowing down plasmons at the taper apex. The measurements also evidence a substantial increase of the lifetime''of the electron gas temperature at the apex. This interesting effect is interpreted as resulting from an intricate heat flow at the apex. The ability to harness the lifetime''of hot-carrier gases with nanoscale circuits may provide a multitude of applications, such as hot-spot management, nonequilibrium hot-carrier generation, sensing, and photovoltaics.