Infrared pump-probe spectroscopy provides detailed information about the dynamics of hydrogen-bonded liquids. Due to dissipation of the absorbed pump pulse energy, thermal equilibration dynamics also contributes to the observed signal. Disentangling this contribution from the molecular response remains a challenge. By performing non-equilibrium molecular dynamics simulations of liquid-deuterated methanol, we show that faster molecular vibrational relaxation and slower heat diffusion are decoupled and occur on different length scales. Transient structures of the hydrogen bonding network influence thermal relaxation by affecting thermal diffusivity over a length scale of several nanometers.