If the Emperor Joker storyline is any indication, Superman's shown himself to be very vulnerable to Reality Warping, which is what the Cosmic Cube does. Ultimate Thanos takes this no contest. He could turn Superman's bones into Kryptonite with Transmutation. He could turn Superman into his personal bodyguard and slave with Mental Manipulation, and force him to conquer worlds in Thanos' name. Thanos could lock him into an eternal mental hell where he has to experience the deaths of all his loved ones and see his adopted planet devastated over and over.
The only way Superman wins is that he might be faster than Thanos, and could take the Cube from his hand before he can act, but the thing is: Ultimate Cosmic Cube does not require the user to physically hold it. Thanos has a mental link with it a thousand times stronger than Reed Richards. So even if Superman grabbed the cube and ran with it, Thanos could still use it. But the battle conditions say that their speed is equalized, so that point is null.
Even in a hand to hand fight, Thanos might be his match. Sure we've all seen scenes where Superman's punch liquifies his opponent, so if Superman could punch Thanos hard enough this fight would be over. But Thanos is no slouch in the durability department, taking blows from the Ultimate Thing (who is described as being stronger than regular Thing), plus the Human Torch and Invisible Woman's combined attacks. Thanos could just erect a force field to protect himself. I think the only time we ever saw Ultimate Thanos actually significantly harmed was when he was actually killed, and that took the Cube's power itself turned against him. Oh, and for the record, punching Thanos is a bad idea. It hurt the Thing's hand and seems to have some corrosive quality (Thanos describes it like touching the void).
And if Thano's comment about "bathing in the hearts of stars" is true, heat vision won't do anything either. So the two things that Superman could do to win this fight: namely punching and heat vision are out of the question. For Superman's sake, I hope Thanos just happens to be vulnerable to freezing, but we saw him happily hovering above a planet that he had frozen to 7 degrees above absolute zero; so we know the Cube could protect him from that.