I also believe that from death to resurrection it was literally "three days and three nights" (not "one day and two nights" as some wish to rationalize it). Jona's duration in the belly of the great fish was measured by Jesus as a "three days and three nights" duration.
However, I do not think "heart of the earth" is the grave. Peter's sermon in Acts 2:29-32 says:
29* Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day. 30* Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne; 31* He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption. 32* This Jesus hath God raised up, whereof we all are witnesses.
I think the heart of the earth is in fact hell. And Christ's soul was there three days and three nights, while his body (flesh) was in the tomb where it did not see corruption.
I do not subscribe to that understanding. As a former Atheist - I go by strict interpretation of the scriptures themselves and often look at the original words used to understand their meaning. I spent much time attacking Christianity for all it's inconsistencies with the scriptures and all the pretzel logic to explain traditions grafted into the faith to try and prove God's Word false. Taking the bible at it's own word without any traditions or twists to conform the scriptures to doctrine - I saw that the Bible was indeed God's Word, and unbreakable.
"Hell" as used in Acts 2:29 is the Greek word 'hades'. The term hades in Christian theology (and in New Testament Greek) is parallel to Hebrew sheol (שאול, grave,tomb or dirt-pit), and refers to the abode of the dead.
The Greek word Hades in this usage (11 times to be exact) is "ᾅδης" (Hades). The Greek word to denote the underworld of Greek myth is: ᾍδου, Haidou. Christians wrongly assume that the term 'hades' in the New Testament is a reference to the Greek underworld. The location of 'Hades' (or underworld) to follow tradition, the Greek words are ᾍδου, Haidou, an elision to denote locality: "[the house/dominion] of Hades, the Greek God of the dead.
In the Septuagint (the ancient translation of the Old Testament into Greek), the Greek term "ᾅδης" (Hades) is used to translate the Hebrew term "שׁאול" (Sheol) in Isaiah 38:18. This use refers the term hades to the abode of the dead.
In New Testament Greek, the Hebrew phrase "לא־תעזב נפשׁי לשׁאול" (you will not abandon my soul to Sheol) in Psalm 16:10 is also quoted in Acts 2:27 as "οὐκ ἐγκαταλείψεις τὴν ψυχήν μου εἰς ᾅδου" (you will not abandon my soul to Hades).
I believe Jesus was in the tomb (or Sheol/grave) for 3 days and 3 nights, just as He said. His flesh did not see corruption as He was resurrected to Glory after the third day, rising again to the Life eternal we hope for in Him. Thus the prophecy in Psalms 16:10 was used again in Acts 2:27 to prove Jesus' Messiahship to the unbelieving Jews.