If you have never studied this doctrine of the divine impassibility, I encourage you to read the following history by Dr. Robert Culver. It is very good and thought provoking:
Here is an important excerpt from the paper:
Impassibility comes into our language as translation of the Greek word apatheia in the writings of Church fathers, according to the Oxford English Dictionary. Apatheia, despite the obvious etymological connection with apathy and apathetic in modern English, (Pelikan) started out as meaning “the state of an apathes” (alpha privative, plus pathos) without pathos or suffering” (Liddell and Scott Lexicon). Among the Greek Fathers pathos or passion was the right word for the suffering of Christ, as it still is. So in theology to be impassible means primarily to be incapable of suffering. Early theology affirmed that in heaven our resurrected bodies will be pathes in this sense. The word came to be extended to mean incapable of emotion of any kind and beyond that, apathes (impassible) in important theological discourse meant without sexual desire (Gregory of Nyssa, The Great Catechism, chap. xxxv, “Nicene and Post-Nicene Fathers, Second Series,” edited by Philip Schaff and Henry Wace, 1910, ii, 5, pp. 502-504). As applied to God, incapacity for any emotions sometimes is meant. We will return to this. The twelfth canon of the Second Council of Constantinople (553, Fifth Ecumenical) seems to say Christ on earth was impassible in the sense of “longings (passions, presumably sexual) of the flesh” (Henry Denzinger, The Sources of Catholic Dogma, trans. R. J. Deferrari, Hersler Book Co., 1954, 224).
In this paper I am interested mainly in the question of whether or not the divine nature is capable of emotion, including, in a secondary way, the experience of suffering.