In addition to the previous post, there are a few more aspects to this paradox:
1) "Love" is an emotional experience for this speaker, whereas "thinking" is intellectual. This speaker may be in the early stages of a relationship--the infatuation or puppy love stage--and only feel butterflies with his love is within contact.
Or, the speaker may be in a long-term relationship--married for several years--and has gotten so used to his mate that s/he no longer needs to "think" about him/her. This is a kind of symbiotic relationship, where each partner lives inside the other--in this case, the heart more than the brain.
2) "Love" and "memory" may be antithetical. Again, "love" may be a hands-on, physical experience for this speaker: s/he only loves in time, when the other is present. After all, how can someone "love" a memory of another? Does not "love" diminish over time if there is no contact?
That is a good question and paradoxes are wonderful things, because they make you think! With that said, one must also be open to the fact that a paradox may actually a contradiction.
I think one of the ways in which we can understand this paradox is by thinking of a possible scenario where this statement might be true. Here are two possibilities.
1. A person has a mental disorder and has a hard time remembering. Older people might experience this. An example comes from the movie "the Notebook."
2. I can see this taking place, if a person works really hard for another person and that work requires a high level of concentration.