Yes, God certainly cares about what we think, just as He cares about what we do -- if not more so. In fact, some of Jesus' strongest words were directed at people who were outwardly righteous but corrupt in their thoughts. He called them "whitewashed tombs, which look beautiful on the outside but on the inside are full of dead men's bones and everything unclean" (Matthew 23:27).
Why is God concerned about our thoughts? One reason is because behind everything we do is a thought -- for good or for evil. Even if we aren't aware of it at the time, we never act unless we've first thought about it. For example, if our thoughts are always selfish, our deeds will be selfish also. Jesus warned, "For out of the heart come evil thoughts, murder, adultery, sexual immorality, theft, false testimony, slander" (Matthew 15:19).
God wants our thoughts to be pure -- but how is that possible? One way to safeguard our minds is to avoid anything that fills our minds with corrupt or evil thoughts. In addition, we need to fill our minds with that which is good, through prayer and the study of God's Word, the Bible.
Begin by committing your whole life -- including your mind -- to Jesus Christ. Then ask Him to teach you more and more about His love, so that Christ becomes the focus of your mind and heart every day.