Control of intervalley scattering in Bi$_2$Te$_3$ via temperature-dependent band renormalization

The control of out-of-equilibrium electron dynamics in topological insulators is essential to unlock their potential in next-generation quantum technologies. However, the role of temperature on the renormalization of the electronic band structure and, consequently, on electron scattering processes is still elusive. Here, using high-resolution time- and angle-resolved photoemission spectroscopy (TR-ARPES), we show that even a modest ($\sim$15 meV) renormalization of the conduction band of Bi$_2$Te$_3$ can critically affect bulk and surface electron scattering processes. Supported by a kinetic Monte Carlo toy-model, we show that temperature-induced changes in the bulk band structure modulate the intervalley electron-phonon scattering rate, reshaping the out-of-equilibrium response. This work establishes temperature as an effective control knob for engineering scattering pathways in topological insulators.