I've been hearing this a lot lately, but I can't seem to find anything to disprove (or prove) this claim. I know that a weak signal means the phone produces more radiation (which makes sense), but a lot of people I know constantly talk about how using a mobile phone while it is being charged is dangerous, because when you plug it in it produces a lot more radiation.
Perhaps it's an extension of this rumor about low battery causing a similar effect. Also, note I'm not talking about the dangers of the phone exploding or anything like that, because while that does happen, it seems that those are most probably related to counterfeited phones of questionable quality.