Some nouns are weak which means they decline in the singular just as you'd have in the plural.
Just to make it clear, there are many ways of forming the plural and remember that not every (e)n ending should automatically register a plural in your mind. One of the ways of forming the plural is adding -(e)n of course (die Frau > die Frauen) but you have -(e)n endings because of declension. Declension example: one solid rule is adding -(e)n for dative plurals:
E.g. the plural of der Monat is die Monate [plural nominative, adding an -e in this case] which in turn you'd have to add a -n ending to in order to form the dative plural: die Monate [nom] > die Monate [akk] > den Monaten [plural dative]. Similarly, that -n or -en ending in plural Monaten is taken on by certain singular nouns that happen to be "weak" (they are all masculine). Examples of weak nouns include masculine nouns ending in e (amongst others) e.g. der Junge > den Jungen > dem Jungen > des Jungen (all singular).
Another peculiarity of this "having an effect on the noun" syndrome is found in the Genitive where des from der masculine or das neuter modifies the noun by adding -(e)s: der Rat becomes des Rats and das Buch becomes des Buches. Weak masculine nouns override this rule by having their own special case scenario as above with der Junge > des Jungen.
There are exceptions e.g. der Name in the genetive combines both effects: the -(e)n being a weak masculine and -(e)s (genitive): so that you have des Namens. That is exactly the case with des Herzens which is the only non-masculine (neuter) noun to act like weak masculine nouns (in the genitive.. yet it has a unique declension).
This reply is, as usual, utterly impenetrable. Let me try to translate it into English. Plurals ending in -e form their genitive plural with -en. For example, der Monat, the month forms it's nominative plural as die Monate and its dative plural as der Monaten. There is a class of masculine nouns ending in -e known as "weak" nouns, for example der Junge, the boy. These form their genitive singular in -en, des Jungen, of the boy The "des Herzens" in this case demonstrates the irregular declension of "herz", heart. Herz forms its singular genitive irregularly, des Herzens, of the heart. Another noun which forms its genetive singular irregularly in this way is der Name, the name. Its genitive singular is des Namens, of the name.
The genitive plural is "der Herzen"; I believe that your sentence would be "Das ist der Weg der Herzen.".
See this link for the declension: http://en.wikipedia.org/wiki/German_nouns#Irregular_declensions
Would "That is the way of the heart" and "That is the way to the heart" be translated the same way in German? To my ear, the second is more common in English (and that is how I translated the German phrase.....incorrectly, of course). They do mean something different, so perhaps I am way off base.
"The way of the heart" is a very old English expression, which may explain why you were not aware of it.