In attempting to reconcile AP principles with Catholic doctrine one must address the concept of punishment and rewards. Naturally, the question arises, "Does God reward and punish sinners?"
Catholic doctrine teaches that Heaven is a free gift of God, the good do not deserve it, nor can they earn it. Therefore, one cannot think of Heaven in terms of a reward.
The opposite of reward is punishment. The dictionary defines punishment as "a penalty inflicted for an offense, fault, etc." But God does not inflict Hell on unrepentant sinners. Quite the contrary! Hell is but the truly natural consequence of a resolute turning away from God--a conscious decision to orient oneself horizontally rather than vertically--to worship oneself, rather than the Almighty Creator on whom one depends for his very existence.
The souls in Hell cannot be happy in Heaven. Their failure to repent in the end is but their refusal to forgive God for loving them enough to create them. Such close proximity to the object of their hatred would be far more unbearable than any pain Hell can offer. In fact, since God is everywhere, even in Hell, and loves every one of us always, the pain experienced by the souls in Hell is because of His presence there and the certain knowledge that He still loves them. The souls of the unjust can no sooner sustain such close proximity to the Almighty, Perfect God than a dry leaf could sustain itself in the heat of the sun. Hell is God's merciful provision for those who refuse to be loved by Him.