That is what I thought. However, I read that Cardinal Roger Mahony has said that there is a cat heaven. And on this Catholic Answers Forum, there have been serious discussions about how various animals go to heaven.
Here is a transcript of what Cardinal Mahony believes on this:
"Cardinal Mahony: I have two cats: Rafael and Gabriel, named after the Archangels!!
Madeline P.: great names
Alex H.: what wonderful names
Jillian J.: O what pretty names!!
Carolyn H.: I love those name especially Rafael
katy t.: We celebrate the blessing of the animals every year, we all bring our pets and they receive a blessing
Cardinal Mahony: Animals are a great gift of God for all of us! Our pastor at the Cathedral has a dog, and he gets along great with my cats.
Jillian J.: what happened to Miguel?
Cardinal Mahony: Miguel went to Cat Heaven in 2004".
Please see: recongress.org/chat2007s.htm
So if cats and other animals go to heaven, then why would not a Neanderthal go to heaven also, even if he did not have a human soul?