Thomas Aquinas, Summa Theologiae, supplement to the third part, question 99, ARTICLE 1. Whether by Divine justice an eternal punishment is inflicted on sinners?

(The method of the Summa Theologiae is to state objections, and then reply to them)

“Objection 6: .... it would seem out of keeping with Divine justice that sinners should be punished for ever.”

Reply, attempting to justify the eternal burning of the wicked:

“.... because they sinned against an eternal good by despising eternal life.” 

(Because they despised the eternal reward [eternal life] the wicked must burn eternally)

“.... the punishment of mortal sin is eternal: because thereby one offends God Who is infinite.” 

(Sin offends God who is eternal; therefore punishment [by burning] must be eternal)

" .... they will burn to some purpose, namely that the just may all both see in God the joys they receive, and perceive in them the torments they have escaped ...." 

(The redeemed in Heaven will look on the wicked burning in hell and appreciate their own joy)

"Almighty God .... on account of His justice. He is for ever unappeased by the punishment of the wicked." 

(The wicked must burn forever because God will never be appeased by their punishment)