Your mind and heart are not so separate as your question would suggest. Not that they are the same thing but simply that they are connected and that consistent compartmentalization cannot be maintained.
To say in your mind that you believe something that you don't open your heart too, as you put it, is simply to lie to yourself and to fake your own consciousness. Generally speaking, your heart will follow the conviction of your mind as will your body. To the extent it won't for the Christian is what we refer to as "the flesh". Paul spoke to this explicitly and makes it clear that the battle is won or lost IN YOUR MIND - not your heart.
Romans 7:14 For we know that the law is spiritual, but I am carnal, sold under sin. 15 For what I am doing, I do not understand. For what I will to do, that I do not practice; but what I hate, that I do. 16 If, then, I do what I will not to do, I agree with the law that it is good. 17 But now, it is no longer I who do it, but sin that dwells in me. 18 For I know that in me (that is, in my flesh) nothing good dwells; for to will is present with me, but how to perform what is good I do not find. 19 For the good that I will to do, I do not do; but the evil I will not to do, that I practice. 20 Now if I do what I will not to do, it is no longer I who do it, but sin that dwells in me.
21 I find then a law, that evil is present with me, the one who wills to do good. 22 For I delight in the law of God according to the inward man. 23 But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members. 24 O wretched man that I am! Who will deliver me from this body of death? 25 I thank God—through Jesus Christ our Lord!
So then, with the mind I myself serve the law of God, but with the flesh the law of sin.
It is not our hearts we should be trusting (Jeremiah 17:9) but rather the conviction of our minds as Paul goes on to say in Romans 8...
Romans 8:5 For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit, the things of the Spirit. 6 For to be carnally minded is death, but to be spiritually minded is life and peace. 7 Because the carnal mind is enmity against God; for it is not subject to the law of God, nor indeed can be.
Romans 12:2 And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God.
Lastly, getting back to your original point, I said...
"To say I believe is to connect to Him Spiritually. (Yes, I noticed the capital 'S'.)
You cannot do one without the other, unless you're just lying to begin with."
This is exactly what Paul teaches in Romans 10...
Romans 10:10 For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation.
And so, I say again, you cannot do one without the other, unless you're just lying to begin with.
Resting in Him,
Clete