Do not say, 'But it is hypocritical to thank God with my tongue when I don't feel thankful in my heart.' There is such a thing as hypocritical thanksgiving. Its aim is to conceal ingratitude and get the praise of men. That is not your aim. Your aim in loosing your tongue with words of gratitude is that God would be merciful and fill your words with the emotion of true gratitude. You are not seeking the praise of men; you are seeing the mercy of God. You are not hiding the hardness of ingratitude, but hoping for the in-breaking of the Spirit.

Thanksgiving with the Mouth Stirs Up Thankfulness in the Heart

Moreover, we should probably ask the despairing saint, 'Do you know your heart so well that you are sure the words of thanks have no trace of gratitude in them?' I, for one, distrust my own assessment of my motives. I doubt that I know my good ones well enough to see all the traces of contamination. And I doubt that I know my bad ones well enough to see the traces of grace. Therefore, it is not folly for a Christian to assume that there is a residue of gratitude in his heart when he speaks and sings of God's goodness even though he feels little or nothing. To this should be added that experience shows that doing the right thing, in the way I have described, is often the way toward being in the right frame. Hence Baxter gives this wise counsel to the oppressed Christian:

'Resolve to spend most of your time in thanksgiving and praising God. If you cannot do it with the joy that you should, yet do it as you can. You have not the power of your comforts; but have you no power of your tongues? Say not that you are unfit for thanks and praises unless you have a praising heart and were the children of God; for every man, good and bad, is bound to praise God, and to be thankful for all that he hath received, and to do it as well as he can, rather than leave it undone.... Doing it as you can is the way to be able to do it better. Thanksgiving stirreth up thankfulness in the heart.

John Piper