[chris (OP)]

How do light waves propagate through transparent media? What's going on when this happens?

[CZARCAR]

the media gets hotter

[Cheese2001]

Not sure how in-depth an answer you are looking for... but here goes.  The speed of light is a constant around 3.0 x10^8 m/s in a vacuum.  It is close to that value in air, but it is truly slightly less.  As light passes through a transparent medium, like air or glass, it slows.  The rate of slowing is proportional to the frequency.  Which is why white light entering a prism, exits as a rainbow.  The glass slows each frequency of the incident white light at a slightly different rate.  So when it exits the prism and the entire wave speeds up to the speed of light in air, the light has spread out in spectrum.  The effect is well defined by Snell's Law, and there is a very good discussion at:  http://en.wikipedia.org/wiki/Prism_%28optics%29 [nofollow] .