Apollinarianism was the heresy taught by Apollinaris the Younger, bishop of Laodicea in Syria, about 361. He taught that the Word of God, which became the divine nature of Christ, took the place of the rational human soul of Jesus and that the body of Christ was a glorified form of human nature. In other words, though Jesus was a man, He did not have a human mind. He taught that the mind of Christ was solely divine.
This heresy believed Jesus was human, and only His mind was divine; this contradicts scripture, and though it may be difficult for us to comprehend, the Bible is clear that the incarnation of Jesus was entirely man and fully God.
As with the heresy of Adoptionism, any time a belief or teaching removes Jesus from the Godhead or Trinity or states that Jesus was not God contradicts the Bible and what Jesus taught.
"For in Christ all the fullness of the deity lives in bodily form,10 and in Christ you have been brought to fullness. He is the head over every power and authority." 2 Colossians 2:9-10
The fact that Jesus is entirely man and fully God is known as the Hypostatic Union.
Jesus as God
He is worshipped - Matthew 2:2, 11; 14:33
He is prayed to - Acts 7:59
He is sinless - 1 Peter 2:22; Hebrews 4:15
He knows all things - John 21:17
He gives eternal life - John 10:28
All the fullness of deity dwells in Him - Colossians 2:9
Jesus as Man
He worshipped the Father - John 17
He prayed to the Father - John 17
He was tempted - Matthew 4:1
He grew in wisdom - Luke 2:52
He died - Romans 5:8
He has a body of flesh and bones - Luke 24:39
Jesus is God in the flesh (John 1:1, 14, 10:30-33, 20:28, Phil. 2:5-8, Heb. 1:8). He is fully God and fully man (Col. 2:9); thus, He has two natures: God and man. He is 100% God and 100% man.
He never lost His divinity. He continued to exist as God when He became a man and added human nature to Himself (Phil. 2:5-11). Therefore, there is a "union in one person of a full human nature and fully divine nature." Right now in Heaven, there is a man, Jesus, who is our Mediator between us and God the Father (1 Tim. 2:5).