A Logical Explanation for Purgatory

Lets just imagine that there was just Heaven and Hell, no Purgatory. The Bible teaches us that nothing unclean will enter Paradise. This makes sense because it can't be paradise if there are sinners in it. Thus, if there was no purification of these sinners then that means that they would all go to Hell even if their sins were not serious. We know that God's love is endless and he would not send someone to just because they did some small thing during their lifetime. Thus, there must be some kind of purification before we enter Heaven, which is Purgatory.