  We apply an intense infrared laser pulse in order to perturb the electronic
and vibrational states in the three-dimensional charge density wave material
1$T$-VSe$_2$. Ultrafast snapshots of the light-induced hot carrier dynamics and
non-equilibrium quasiparticle spectral function are collected using time- and
angle-resolved photoemission spectroscopy. The hot carrier temperature and
time-dependent electronic self-energy are extracted from the time-dependent
spectral function, revealing that incoherent electron-phonon interactions heat
the lattice above the charge density wave critical temperature on a timescale
of $(200 \pm 40)$~fs. Density functional perturbation theory calculations
establish that the presence of hot carriers alters the overall phonon
dispersion and quenches efficient low-energy acoustic phonon scattering
channels, which results in a new quasi-equilibrium state that is experimentally
observed.
