If anything, the Judge should be the Absolute Supreme, but if He did this, then we'll all be dead. God is not a school teacher, but a loving mother/father; a weaver or potter whose only purpose - speaking loosely - is to weave, mould ... it is compassion, but which may appear like Justice -- a disguised form of Love.
We keep 'thinking' you say. That is correct. Thinking is of the mind and it is the place where judgement takes place. The heart we speak of is generally related to the emotions. The spiritual Heart; the psychic Heart, works for the manifestation of the Supreme, usually in the same way as the soul does. the Soul is the highest member of the human psyche.
God never judges, neither does the Heart. Judging is a thought process coming from the division-separating-mind; the analytical and scholarly mind. Through meditation, we can learn to 'feel' with the Heart. It is infinitely higher than the mind. Much Love.
P.S. Some kinds of judgements are necessary for survival: crossing the road; walking in the dark; where we sit in a train, domestic analysis and a few more ... it will increase or decrease based on our individual level of inner growth at any given moment.