I nearly burnt down my house. I melted one of my favorite clocks too. Now I will NEVER have a light that generates heat that is note WIRED DOWN or hung from a sturdy hook in the cieling. It's just not worth losing your house over to be too lazy to do this. You can use a hammer and nail to pop a hole in the lip of the fixture and some coathanger wire to wire it right to the lid (or even a twist-tie), or put in plant hooks from the ceiling and tie off the cord of the light to them so it hangs to the right height above the cage.
SO MUCH SAFER. Don't kill yourself or your family for just something as silly as being too lazy to secure the lamps safely! I never would have even thought of it, though, until it nearly happened to me.