"Ich spreche mit dem Herzen."
Translation:I speak to the heart.
No, it is not. It is simply wrong and not used in German language at all, and if you try Germans will ask you what you mean with that. Correct ways of telling someone that you say something from the bottom of your heart look here please: http://www.linguee.de/deutsch-englisch/uebersetzung/aus+vollem+herzen.html It is too long to explain, but don't use that DUO sentence is wrong, you cant speak with you heart. I am a native German speaker. Cheers
Is this an idiom? Herzen seems to be plural here, though the translation in English is singular
But don't want to tell anyone, that "Ich spreche mit dem Herzen." is a proper German sentence, do you? As it is impossible to speak with the heart, and there is no idiom in German, this sentence has no meaning and is wrong. There are hundreds of ways in German to tell that you are speaking/talking from your heart, - but none "with your heart" :-)