One thing to keep in mind is that objects that are bound gravitationally actually revolve around each other around a point called a barycenter. The fact that the earth looks like its revolving around the sun is because the sun is much more massive and its radius is large enough that it encompasses the barycenter. This is a similar situation with the Earth and Moon. If there were three bodies, where two bodies were of similar size (like a binary star system plus a massive planet) then an analysis of three body systems shows that there are stable configurations where the objects will be in very complicated orbits where it would be difficult to say one orbits the other.
Update: The short answer is yes, it is possible when you look at the complete dynamical system, for the reasons stated above. More evidence of this can be found in the study of regular star orbits where very complicated orbits are possible and can be stable. Currently the cut off for classification of a planet and a brown dwarf is 13 Jupiter masses, which is arbitrary to some degree. The lightest main sequence stars have a mass of 75 Jupiters. This will put the barycenter well outside the radius of either body for binary systems.
A quick check of the two body system using the equation:
$$R = \dfrac{1}{m_1 + m_2}(m_1r_1 + m_2r_2)$$
Setting $m_1 = 75$, $r_1 = 1$, $m_2 = 13$, $r_2 = 2$ gives:
$$\dfrac{75 + 26}{75+13} = 1.147$$
Indicating a barycenter at roughly $\dfrac{1}{7}$ the distance between the objects. More bodies will cause more complicated orbits, where again, it would be difficult to say which object orbits which. It should be noted that if the system was composed of 3 objects, 2 of which had similar mass, it would be possible to develop a system that appears to have two larger objects orbiting a third smaller object. A quick check reveals:
$$R = \dfrac{1}{m_1 + m_2 + m_3}(m_1r_1 + m_2r_2+ m_3r_3)$$
Setting $m_1 = 75$, $r_1 = 1$, $m_2 = 13$, $r_2 = 2$ $m_3 = 75$, $r_3 = 3$ gives:
$$\dfrac{75 + 26 + 225}{75+13+75} = 2$$
Whether such an orbit system is realizable when you consider the full dynamics of a natural system is debatable, but I am not aware of a specific proof that would rule it out.
UPDATE
It should be noted that there are new periodic solutions to 3-body problems when the objects have the same mass.
We need to both comfortable temperatures and an energy source that has a far lower entropy per unit energy compared to energy from our local environment. Sunlight provides for such a low entropy energy source, this is needed to keep lifeforms (which are ultimately processes that are far from thermal equilibrium) alive. Without sunlight you can use reactive chemicals, which is good enough for primitive microbes but lethal for complex life.
Best Answer
It's pretty unlikely, but yes, theoretically it's possible.
That would be one of the very few scenarios where something like this could form. Maybe. It depends on the density fluctuations of the water ejecta. You need a condensation center to gather a large mass of water and get the planet started.
A cloud of stuff contracting under its own gravity will definitely heat up. But here's the thing - it does not matter whether the water is solid, liquid or gas. It would collapse just the same. Gravity is stronger. Doesn't matter whether is cold as ice, or boiling like crazy.
Once it's a small sphere of water in some form, more complex phenomena will take over. See below.
Maybe some heat will be provided by the initial collapse. Maybe it does have some radioactive impurities which will heat it up. But anyway, over a very long time it would tend to cool down.
In general, the core would be an exotic form of high-pressure ice, no matter what the temperature - water is solid at very high pressure, even if you elevate the temp a lot. Above that there will be a layer of liquid water, if the whole planet has enough warmth, or just plain old ice if it's too cold altogether. The surface might be solid again, cold ice (if the planet is wandering alone in space), or liquid (if it's close to a star). There may be a water atmosphere above, either wispy and thin (cold planet) or thick (warm planet).
http://www.lsbu.ac.uk/water/phase.html
When the escape velocity of water molecules is bigger than the average thermal speed, the body is stable. In other words: Warm planet - needs to be bigger to keep the water in. Cold planet - it can be smaller.
A small chunk of ice could survive for quite some time in outer space before sublimating to nothing. A Moon-size blob of ice would probably be stable forever. But if there's warm water on the surface, and a thick water atmosphere, it would probably require an Earth-like mass (and gravity) to keep the water from escaping.
If it's life that doesn't need dry land and ocean bottom to survive, then yes.
There's a type of exoplanet that is similar to what you describe. Not identical, but kind of close:
http://en.wikipedia.org/wiki/Ocean_planet