6" tall is plenty. Corns are really only interested in floor space. Make sure you make lots of holes for ventelation. A good rule is if there is water condensing on the sides, you don't have enough holes.
You can use a small drill bit (3/16") if you use high rpms and light pressure when you drill. If you push too hard, the rubbermaid will crack when the bit pops through.
Another way is to use a soldering iron. If the point is about 3/16 in dia you can melt through the plastic. This is a little slower but you are less likely to crack the plastic.
The UTH should never get hot enough to hurt the plastic. If you are melting plastic, it won't matter cause your snake will be dead.