Herz has irregular singular declension and is the only noun of its kind.
The genitive singular generally takes the ending -ens: des Herzens.
The dative singular traditionally takes -en: dem Herzen. This form is still the only accepted standard form in many—more or less fixed—expressions, such as im Herzen, von Herzen, zu Herzen, Operation am offenen Herzen ‎(“open-heart surgery”), mit halbem Herzen ‎(“half-heartedly”), and more.
Otherwise, the forms dem Herzen and dem Herz are both acceptable. The latter is predominant in speech, while the former remains the more established form in writing. — But only the bare form is common for Herz as a card suit or a term of endearment, as well as in the phrase mit Herz ‎(“good-hearted”).