This comes up in a number of contexts, probably most common with reading the Bible, but other circumstances also. The argument goes sort of like this: 1) I don't particularly have a strong desire to ______. 2) God looks at the heart and not the outward appearance. 3) Therefore, I don't want to appear to be a hypocrite so I won't do ______.
To which we both agreed that the person should do _____ anyway, even if they "don't feel like it." The reason why this isn't inconsistent with the fact that God looks at the heart is because what we demonstrate when we obey anyway is that we value obedience to God more than simply feeling good about something. Of course in an ideal world without sin we'd always be able to delight ourselves in the word of God every morning, but sometimes that doesn't happen. But we still love God enough and believe his promises enough to continue to go back to the Word, even if it's not sheer delight.
When the Bible says that God looks at the heart, I think the emphasis is much more on "who are you trying to please?" If a person is always reading his Bible in public in order to garner public approval, then that is all he's going to get. But if a person privately reads his Bible even if he "doesn't feel like it," then that is true evidence that "I believe God more than I believe my heart." And with that, God is honored.