what happens inside linear polarizer sheet (at microscopic level) when unpolarized light falls on it? (1) What happens at microscopic level when unpolarized light falls on a linear polarizer sheet ? i.e. Due to what thing inside polarizer sheet, only those EM waves are passed whose plane of vibration of electric field is parallel to transmission axis of polarizer sheet ?
(2) Consider experiment of measuring degree of linear polarization of light coming from an incandescent source of light. First light falls on linear polarizer and then analyzer (which is again a linear polarizer). Light blocked by polarizer is absorbed by polarizer and heats up the polarizer (some of the blocked light will be reflected). Does this affect the measurement of degree of linear polarization ?
 A: (1) I assume you are referring to a Polaroid sheet (specifically H-sheet), which is the most common form of dichroic polariser; that is, it linearly polarises light by selective absorption of the electric field component in certain directions. 
On the molecular scale, this phenomenon is a result of the alignment of polyvinyl alcohol (PVA) chains within the material, which have been treated with an iodine compound to strongly absorb light with an electric field parallel to their orientation. Specifically, the iodine atoms provide electrons which can move easily along the aligned chains, but not perpendicular to them. Hence, light waves with electric fields parallel to these chains are strongly absorbed because of the dissipative effects of the electron motion in the chains.
(2) I don't imagine the heat would have an appreciable effect, however you will probably find most precision polarisers (which are comprised of more than just polaroid sheet) have a specified operating temperature range.
A: The polaroid sheet consists of a polymer into which a dye, originally iodoquinine sulfate, is dissolved. The film is aligned by stretching, and this causes the molecules of iodoquinine to align along the pulling direction. Photons are absorbed by the iodoquinine whose electric (or transition) dipole is aligned along the long axis of the molecule, but only if the photon's polarisation is in the same direction as the transition dipole (with an absorption probability of cos(theta)^2 with theta the angle between the transition dipole and polarisation ). Thus the sheet acts as a polariser. 
However, it is not as good as using a Glan-Laser type polarising cube (two prisms form a cube) as it absorbs a lot of light and the extent of polarisation is not that good. A good polarising cube can reach 1 part in a million purity not 1% typical of a polaroid film. 
Heating the film will clearly destroy the alignment of any entrapped molecules and so destroy any polarising effect initially most probably by rotational diffusion of the iodoquinine molecules.
