Cats have the basic senses that most living creatures have; Sense of smell, touch, sound, taste, and sight. The biggest difference from us and cats is that we have a soul and a spirit, where cats only have souls. The difference between the soul and the spirit is conflicting emotions. The soul governs emotions, both good and bad. The spirit on the other hand is the head seat, and governs the soul and the body. With a cat, because they only have a soul, they base emotions solely on natural, God-given instincts. They are able to form relationships, become happy, jealous, and so on. Since we have spirits, we have the conflict inside us to choose what is right and what it wrong based outside of instincts or common laws of creation. We have the laws and morals of God in our hearts and learn on higher levels of authority, where cats (and other animals) only use only their soul.
In essence, the soul is merely the mind. Since the spirit of each man/woman is the highest authority of a being, that is what continues to live on after physical death. The soul, or mind, is the distinctive emotion behind the spirit, it can be changed upon experience, hinder growth and learning, and can be manipulated and tricked based on experiences both past and present. The spirit is the true living individual in the body. It is what gives us the ability to choose freely for ourselves. Cats, on the other hand, only work and choose what they do based on instincts in their mind.
So based on the Holy Bible, cats and other animals cannot be sent to hell or heaven because that is where the spirit goes. That is not to say their soul does not live on. The mind of each cat distinguishes them from each other. It allows various personalities and unique characteristics. Because God is love and love is God, the purest and most highest form, He knows what is in our hearts. We must remember there will be a new physical life, we will have new bodies and a whole new (refurbished and holy) world to live on after heaven. This is where God’s true love, I feel, will make it possible for us to reunite with our lost cats and other animals again.
So the short answer to the question is no, cats do not go to heaven, but that doesn’t mean God will not allow their soul to live on in New Jerusalem. The Bible never states that they are gone forever, nor does it say they don’t have a special heaven for themselves. Love makes all things possible, and God is love after all.