The Short Answer:The short answer is no, Satan cannot read our minds. While we learn in Scripture that Satan is powerful and influential, he is not all knowing, or omniscient. Only God has the ability to know all things.
Furthermore, there are no examples in the Bible of Satan reading someone's mind.
The Long Answer:Satan and his demons are fallen angels (Revelation 12:7-10). In Ephesians 2:2, Satan is called "the prince of the power of the air."
So, the devil and his demons do have power--the same power given to angels. In Genesis 19, angels struck men with blindness. In Daniel 6:22, we read, "My God sent his angel and shut the lions' mouths, and they have not harmed me." And angels can fly (Daniel 9:21, Revelation 14:6).
But no angel or demon has ever been depicted in Scripture with mind reading abilities. In fact, the encounters between God and Satan in the beginning chapters of the book of Job, strongly indicate that Satan cannot read the thoughts and minds of humans. If Satan had known the mind and heart of Job, he'd have known that Job would never curse God.
Understand, however, while Satan cannot read our minds, he does have an advantage. He has been observing humans and human nature for thousands of years. This fact is evidenced in the book of Job as well:
"One day the members of the heavenly court came to present themselves before the Lord, and the Accuser, Satan, came with them. 'Where have you come from?' the Lord asked Satan.
"Satan answered the Lord, 'I have been patrolling the earth, watching everything that's going on.' " (Job 1:6-7, NLT)
You might even say that Satan and his demons are experts in human behavior.
Satan certainly has a fairly good idea how we will react to temptation, after all, he has been tempting humans since the Garden of Eden. Through ceaseless observation and long experience, Satan and his demons can usually guess with a high degree of accuracy just what we are thinking.
Know Your EnemySo, as believers it's important that we get to know our enemy and become wise to Satan's schemes:
"Be sober-minded; be watchful. Your adversary the devil prowls around like a roaring lion, seeking someone to devour." (1 Peter 5:8, ESV)
Know that Satan is a master of deception:
"He [Satan] was a murderer from the beginning, and does not stand in the truth, because there is no truth in him. When he lies, he speaks out of his own character, for he is a liar and the father of lies." (John 8:44, ESV)
And know, too, that with God's help and the Holy Spirit's power, we can fend off Satan's lies:
"Submit yourselves therefore to God. Resist the devil, and he will flee from you." (James 4:7, ESV)