The spirit returns to God and the body returns to dust.
SOUL AND SPIRIT IN DEATH - Ecclesiastes 12:7 says the body returns to the dust and the spirit [or breath of life] returns to God. Job 27:3 tells us that the spirit is the same as God's breath of life or His power.
Psalm 146:4 (KJV) says, "When their spirit departs, they return to the ground; on that very day their plans come to nothing." The dead do not praise God, Psalm 115:17. The dead do not know anything, Ecclesiastes 9:5, "For the living know that they will die, but the dead know nothing."
RESURRECTIONS - There are two resurrections-one to life and one to eternal condemnation. John 5:28-29 (NIV). "Do not be amazed at this, for a time is coming when all who are in their graves will hear his voice and come out-those who have done good will rise to live, and those who have done evil will rise to be condemned."
You take away the breath, that spark of life which comes from God and the body will return to dust (or sometimes to ashes in the case of cremation). What happened to the soul? It just ceases to be until God comes at the resurrection and puts it back together again. At that time the dust and the breath of life are reunited and then you have a life, a live person or live soul again.
You need to define what you mean by "heaven". According to Jesus (Luke 16) after death (which is a separation - what we call dying is the separating of the spirit from the body James 2:26 the body without the spirit is dead) the spirit goes to Hades. Some would call this heaven or hell (refer to the comfort/torment that they found themselves in) but this is only a temporary state until Jesus comes and the judgment occurs and the eternal heaven/hell begins
When we die, the body rots. The soul goes somewhere until a guy tells us if we were nice we enter the pearly gates, if we were very naughty we go to the furnace just like an overcooked steak, or if we were somewhere in between, we get barbecued medium rare, then go to the pearly gates later. Lol.