Do plastic covers for the macbook trap heat? Are they safe?

Anything that prevents moving air from coming into direct contact with the aluminum surface of the machine, particularly its lower portion where most of the heat is generated, will inevitably reduce the efficiency of its radiant cooling. When you aren't pushing the machine hard, that won't make a big enough difference to matter. When you are, it will. I don't recommend using any kind of skin, jacket or case -- most users imagine these things provide much more protection than they actually do, and it gives them a mistaken idea that they can be less careful than they really need to be. At best, a "hard case" protects only against superficial cosmetic scratches -- nothing more.

one way to test to see if it is causing your mac to overheat would be to install the iStat widget. Use it in the exact same manner with and without the case and see if there is a dramatic change in temperature.