You shouldn't be worried. Because of the low low energy of radio waves, all chemical transitions they could cause in your body are already happening due to random thermal motion.

If the amplitude is high enough, though, radio waves can still move ions around. So it's possible that standing next to an AM antenna would have some psychoactive effects, similar to transcranial magnetic or DC stimulation (though the existence of a similar effect for RF, that shows up before the heat input becomes dangerous, is far from certain). But these would be be chemical changes and have nothing to do with cancer.

Also, you're totally right about radio waves warming things up.