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Nanowire lasers can be monolithically and site-selectively integrated onto silicon photonic circuits. To assess their full potential for ultrafast opto-electronic devices, a detailed understanding of their lasing dynamics is crucial. However, the roles played by their resonator geometry and the microscopic processes that mediate energy exchange between the photonic, electronic, and phononic subsystems are largely unexplored. Here, we study the dynamics of GaAs-AlGaAs core-shell nanowire lasers at cryogenic temperatures using a combined experimental and theoretical approach. Our results indicate that these NW lasers exhibit sustained intensity oscillations with frequencies ranging from 160 GHz to 260 GHz. As the underlying physical mechanism, we identified self-induced electron-hole plasma temperature oscillations resulting from a dynamic competition between photoinduced carrier heating and cooling via phonon scattering. These dynamics are intimately linked to the strong interaction between the lasing mode and the gain material, which arises from the wavelength-scale dimensions of these lasers. We anticipate that our results could lead to new approaches for ultrafast intensity and phase modulation of chip-integrated nanoscale semiconductor lasers., Comment: Revised manuscript