Femtosecond optical pump–probe spectroscopy is employed to elucidate the ultrafast carrier nonradiative relaxation dynamics of bare GaAs and a core–shell GaAs/AlGaAs semiconductor nanowire array. Different from the single nanowire conventionally used for the study of ultrafast dynamics, a simple spin coating and peeling off method was performed to prepare transparent organic films containing a vertical oriented nanowire array for transient absorption measurement. The transient experiment provides the direct observation of carrier thermalization, carrier cooling, thermal dissipation and band-gap energy evolutions along with the carrier relaxations. Carrier thermalization occurs within sub-0.5 ps and proceeds almost independently on the AlGaAs-coating, while the time constants of carrier cooling and thermal dissipation are increased by an order of magnitude due to the AlGaAs-coating effect. The concomitant band-gap evolutions in GaAs and GaAs/AlGaAs include an initial rapid red-shift in thermalization period, followed by a slow blue and/or red shift in carrier cooling, and then by an even slower blue shift in thermal dissipation. The evolution is explained by the competition of band-gap renormalization, plasma screening and band-filling. These findings are significant for understanding the basic physics of carrier scattering, and also for the development of flexible optoelectronic devices.