You can't have an ocean that goes on forever downward.
If you pretend that gravity is simply a magical force that acts downward on every object, then you'll run into a bit of a problem as your ocean gets deeper.
Since pressure is a thing, as you descend deeper into the abyss, the weight of the water above you presses down. Assuming that that pressure is proportional to depth ($P(d)\propto d$) then $lim_{d\to \infty}P(d)=\infty$, which basically means that you're gonna have a black hole at the bottom of your world.
Yeah, calculus gets weird when you put in infinity.
Before you get there, though, you're still gonna have some issues with ice. Water has a lot of weird states as it changes in temperature and pressure.

Even at high temperatures, if you compress water enough, it'll turn into ice. All the roman numerals in the diagram describe the different phases of ice, of which there are many. Basically, as you go deeper, water will become ice without needing to freeze.
But wait! What if I heat the water?
At 650K, water and steam are literally the same thing. This is known as the critical point. After this, you have a supercritical fluid, and eventually a plasma.
Ok, massive handwaving time. Let's pretend that there's just a infinite expanse of water that's always the same pressure no matter how far down you go. Blame it on whatever you want, but it's a thing.
Now you've got issues with heat exchange.
It just so happens that water (at sea level, anyways) is most dense at 4°C. Since water freezes below this, it sets up convective cells that shuttle heat downward.
Except that you have an infinite volume. Infinite volume means infinite heat capacity. No matter how energy you put in, eventually physics gets in the way.
Ok, ok, ok. Ignore the density gradient of water. Now what?
Well, at this point, you're all set. You've cannibalized most of known physics and chemistry, and since we don't really have rules for your world that match our own, we can't postulate on what kind of life might form.
Moral of the story? Things get weird when you use infinity.