How do molecules gain kinetic energy from light? I know that molecules can absorb light through electronic and vibrational excitations, which certainly increase the internal energy of a molecule. This idea is always connected to the quantum theory in my head (transition between discreet levels by absorbing a photon with a certain energy etc.)
Now, in the most basic classical picture, temperature of let's say a liquid is basically average kinetic energy of all molecules or their average velocity. 
What I cannot see is how a photon may give a molecule an actual momentum to increase its kinetic energy and consequently increase the temperature? I mean it can excite an electron in the molecule or make it vibrate, but as a whole the molecule does not really move faster. Or is it the acoustic vibrational modes that give the molecule an actual kick? I mean they should still be vibrations, but at least the vibrations which involve moving molecule as a whole.
 A: A photon has momentum $\mathbf{p} = \hbar\mathbf{k}$. This is a vector, so by conservation of momentum, the molecule has to gain momentum $m\mathbf{v} = \hbar\mathbf{k}$ in the proper direction.
During absorption, the energy $hf$ of the incident photon is split in two (or more if there's rotation and vibrations, but let's keep it simple): $hf = \frac{1}{2}mv^2 + \text{levdiff}$. Molecule speed $v$ is defined through $m\mathbf{v} = \hbar\mathbf{k}$, so there is still only one incident energy $hf$ that corresponds to an energy level difference $\text{levdiff}$ (neglecting the spread due to uncertainty, etc.).
A: In addition to the other answer, you are looking for radiation pressure.
Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the object and the EM field. This includes the momentum of EM light that is absorbed or reflected.
Due to the law of conservation of momentum, any change on the total momentum of the waves or photons must involve an equal and opposite change in the momentum of the matter it interacted with.
https://en.wikipedia.org/wiki/Radiation_pressure
