Absorbative polarisers are one way of getting linearly polarised light from an unpolarised beam.
The key idea is that these materials are manufactured such that light can be absorbed in all directions but for a particular one, where it is therefore transmitted.
My question is: how do you 'dump' all the energy that has been absorbed?
I mean, surely you caused an electron to move to the conduction band, and it will somehow try to go down. Can the energy be dissipated via Joule heating?
I do not think there is one method to describe where all the energy goes. This question is similar to an often researched question: "What determines the Laser Induced Damage Threshold (LIDT)". For CW lasers the answer is often (joule) heating. But for pulsed lasers, damage is often caused by dielectric breakdown (i.e. energy going into 're-arranging' a lattice).
An overview meant for determining the safety of optics can be found at Thorlabs http://www.thorlabs.us/tutorials.cfm?tabID=27503. If you follow the sources you will find a more detailed discussion, but not at the reductive quantum level you were hoping for.
