A radiator in a hot water system won't get hot enough to cause a fire. But some fabrics, especially synthetic ones, may not be happy. If you have floor length drapes on these two windows, when they're closed, the radiator would be blocked from doing its job and the room won't be properly warmed. Can you limit the drape length to just below the bottom of the windowsill?

It won't catch fire but it will markedly reduce heat into the room from the radiator.