Dave - good eye.  The sides are 3/4 inch thick.  Overall dimensions are 8 5/16 wide, 10 5/16 long, and 6 1/8 tall (plus top is proud by about 3/8).  

Built so the typical size plastic temporary container for ashes (which are also in a plastic bag apparently) could slide inside.  Per a call to a local company, the typical temporary container is 8.5 x 6.5 x 4.5.  The interior of this box is about 8.75 x 6.75 x 5.5.  I think I may buy an empty temporary container so I can be sure that will work.  Watched one video where a groove had to be added to allow for the temp boxes hinge to clear the side.  

The thicker of the two potential bases I currently have is 3/4 inch.