Some plastics may be able to withstand heat, but you can't usually recognize that from their looks, and you don't know if there may be other problems (such as melamine, which releases toxic chemicals when heated). In theory, I would trust a big manufacturer who markets a plastic pan explicitly as oven-safe, but in practice, I haven't seen such pans. So don't use plastic vessels in an oven.
If you have a cheap bowl you don't mind damaging, you can use it in the oven, but I don't see why, when other materials are much better suited.