The absorbed energy will definitely almost entirely go to heating the plexiglass. The mechanism that leads to chemical change occurs only occasionally and accumulates slowly over time.
You will want to analyze the heating on two time scales: the heating caused by a single pulse and the heating caused by the average power. Generally the single pulse doesn't cause much heating on the short time scale, but 700mJ is a fair bit of energy, so you'll want to check both time scales.
Unfortunately determining the heating is not trivial.
You can make a reasonable estimate for the short time scale. 20ns is very short compared to heat flow. You can approximate that all 700mJ go to heat right where they are absorbed and calculate an upper bound on the fast temperature change before the heat diffuses away. For a quick estimate assume the intensity of the beam is uniform across the beam size. Take the area of the beam times the thickness of the sheet to give a volume of heating. Then calculate:
Temperature rise = Pulse Energy*Absorption / [(Specific heat)*(density)*(Volume)]
You can refine this by being more specific about where the heat is deposited. Break the volume down into little cubes and determine the temperature in the same way, but now using the amount of energy deposited in each cube. This will allow you to take into account the Beer's law absorption in the thickness dimension and the beam intensity profile in the other two dimensions.
The steady state condition due to the average power load is much more complicated. Take the pulse energy times the rep rate of the laser to get the average power load. This goes into the small cubes with the same volume profile you used above. For steady state you have to determine the heat flow to the boundary conditions. What surfaces are being held at a fixed temperature because they are in good thermal contact with a heat sink? Other surfaces are in contact with the room air. Is there sufficient air flow that those surfaces can be treated as a single convective heat transfer constant to air at a fixed temperature? (Usually the case). Now you have to make cubes to represent the plexiglass all the way out to all the known boundary conditions. At each cube interface the heat flow across the boundary is the boundary area time a conduction constant. Internal to the plexiglass the conduction constant is the thermal conductivity. At the boundaries you will have conductivities to the heat baths. You have to find a temperature for each little cube such that the heat flow into and out of each cube is net zero.
Computationally this can be done by the method of finite differences which is easy to understand and set up but slow to calculate, or the method of finite elements which is harder to understand but much quicker. If you choose to do this yourself in truth either will work fine. So what if it takes some minutes to calculate? You would probably learn more doing it with finite differences because it is closer to the actual physical process. You can also watch the temperature profile evolve.
However, the smart money is on finding one of your mechanical engineering friends with access to a program which does Finite Element Analysis such as ANSYS handing them the heat profile and the boundary conditions and letting them get you the temperature profile.
If you would like to do it yourself finite differences isn't difficult, it just requires a lot of book keeping because of the large number of elements. Start with all boxes at room temperature. For each box calculate the net heat flow across all 6 boundaries. Then for a small step in time dt take:
dT = net heat flow*dt/(specific heat * density*element volume)
Update the temperatures and iterate until the temperatures stop changing.
