Okay, so what is the Heart of the Universe described as?
Well...
In Marvel: The End, here's what we get. First we get Thanos' own statements in Issue #5, which is fittingly enough titled "Omnipotence".
"All the theologians were wrong about divine guidance and heavenly judgment. Supreme Power was nothing less than limitless energy, awaiting the first claimant to come along to wield it. There never had been any All-Father, celestial Supreme Will or Almight Self.
That cosmic equation was now chanced and I reveled in my newfound supremacy. With the Cosmic Cube I had manipulated facets of the divine, a very limited experience. The Infinity Gauntlet had granted me mastery of all Time, Space, Power, Reality, the Mind and the Soul, but it was still external control. Now I was all that was and subservient to none. Supreme!"
This strikingly defines the Heart of the Universe as the power of a supreme, "omnipotent" theological god, as opposed to merely absolute control over a universe (Cosmic Cube, which is strictly Universal+ in scale, albeit some have even 2-A feats), or relatively infinite power (The Infinity Gauntlet, which gives the user infinite control over each Gem's domain within its home universe, rendering even the Abstract Beings infinitely inferior. Even an incomplete Gauntlet casually overpowered the Ultimate Nullifier, a weapon that can erase existence on a High 1-B scale, and not only once threatened to erase Multi-Eternity itself, but also gave God Doom trouble once).
No, the Heart of the Universe is literally meant to be Limitless Power.
This conversation between Thanos and Eternity explains it again:
Look at the quotes:
"For these revelations had shown me the error of certain assumptions on my part. Foremost was the conclusion that the previous almighty had been nothing but mindless energy."
Thanos clearly reaches the conclusion that there was a previous Almighty God, and believes himself to be the new one.
Then Eternity shows up and they talk:
Eternity: Greetings, Usurper. I come to demand you relinquish the Supreme Power you have stole!
Thanos: More like it was given to me.
Eternity: Liar!
Thanos: You actually have no clue as to what truly transpires, do you? Your Lord and Master has abandoned you, Eternity, to a dismal fate. Before you sits your only hope for survival.
Eternity: The acquisition of Omnipotence has obviously driven you madder than you already were, Tita. Surrender the Power!
Thanos: And give it to you; to only make an impossible situation worse? I think not.
Eternity: Do you truly believe the universe will allow you to rule it, Titan? I think not.
Thanos: Indeed? Surely, Eternity you must sense that Everything the Almighty was I now am. Did you ever dare demand anything from Him? :
Eternity: No, but...
Thanos: And I, like He was, am now the Author of All that Will Be. My Will is Supreme!
This clearly establishes that the power Thanos now wields is analogue to that of the previous Almighty God, the One-Above-All, even if obviously not complete as it was an a fragment of it. Namely, the aspect of the One-Above-All in the 616 Universe (Hence why it is called the Heart of the Universe).
Thanos even states that he is, by all effects, the new Almighty. And Eternity doesn't deny it, and even hesitates when he tempts it. If Thanos was talking out of his ass Eternity would have immediately pointed it out, but instead Eternity has no counters and just results to anger.
This idea of Thanos being the new Supreme God is re-affirmed again later:
"I acted without thought, as if my response were preordained. In restrospect, I once again consider the deviousness of my predecessor. Was this my moment of triumph or but a face of Another's grand plan?"
It is directly implied that everything that went on in the storyline was the will of the One-Above-All, and outright stated that the power he obtained and wielded was a facet of his power.
And as for the Tribunal?
Literally nothing in the storyline implies that it was an M-Body. They just say it was the Tribunal. In fact, there is evidence of the contrary.
"So now we hear from the top of the food chain, do we?" - Thanos, upon hearing the Tribunal
Were Thanos being met with a mere M-Body of the Tribunal, he would have realized it with his new Cosmic Awareness that outclassed that of the Abstract Entities, and even of the Tribunal, as none of them realized the cosmic wound in the fabric of the universe Thanos perceived. He'd have no reason to say "Top of the food chain" had him been talking to an infinitesimal manifestation of the Living Tribunal.
Okay, now from other storylines...
In the Thanos 2003 Miniseries the Heart of the Universe is once again defined as Supreme Power over the universe it is the Heart of.
"To protect myself from them, I searched out and acquired the ultimate in power, The Heart of the Universe. This turned me into the Supreme Being of this reality, its unquestionable master. Yes: God."
The story would be recapped again in The Infinity Revelation, where it was once again described as supreme power:
Thanos: Which is understandable. I was in the process of gaining unimaginable power.
Adam Warlock: Again becoming Omnipotent, in effect transforming into a Supreme Being.
Also in The Infinity Revelation, due to the events of the story, both a version of Adam Warlock and a version of Thanos end up obtaining the Heart of the Universe (The former), and a comparable power source, the Nexus (The later)
Stuff happens, and each makes a universe be remade in their image. The 616 Thanos and Adam have to revert things back to normal. In the new universe, Infinity is found powerless and imprisoned, and she outright states that the situation is beyond The Living Tribunal's control:
Infinity: You strive and endure, and yet the entire universe ends up turning into a cosmic graveyard.
Adam Warlock: Infinity? The Embodiment of Time bound by dead vines?
Infinity: The moment is thus imprisoned throughout the heavens, Adam Warlock. One world of death followed by another. Nihilism triumphs over hope.
Adam Warlock: Why did you and Eternity let this occur?
Infinity: The decision was made on a level even beyond the Living Tribunal's lofty hierarchical station.
And in the end, after the universe returned to normal, and as a result the universes merged. At the end, the Living Tribunal is shown stating that the events that happened were beyond him:
Infinity: Can you explain to us exactly what we just went through? And why we had to endure the humiliation of the experience?
Tribunal: No, I cannot. My master has provided no explanation of or reason for the event in which we have just participated. Its purpose is as much a puzzle to me as it is to you.
Finally, in the aptly named Infinity Finale, the One-Above-All outright mentions the Heart of the Universe and explains what it is:
Adam Warlock: Above-All-Others is both male and female?
Thanos: So our senses perceive it from moment to moment.
Adam Warlock: Annoying, is it not?
Thanos: No, truly wondrous. It is, in truth, all things and knows all.
One-Above-All: As you yourself partially perceived during your brief experience with Omni-Reality Perception, Tita.
Thanos: Which allowed me a fragmentary glimpse of your power, perceptions and motivations, Grand One.
So in conclusion:
The Heart of the Universe is a fragment of The-One-Above-All's Omnipotent power contained within... the heart of every universe. If a being is to possess it, they will become in effect a Supreme, "Omnipotent" being themselves.
Granted, it is not quite the same level of power as the One-Above-All itself, but in practicality it might as well be. Even Abstract Entities cannot deny it, and even the Living Tribunal himself is beneath the authority of the being who wields such power, as stated by both Infinity and himself.
High 1-B given its lofty origin and cosmic authority fits.