Q:

Drop a star in a river

I (as I am sure you will be able to tell) know very little about nuclear physics, so please understand if something here seems dumb or obvious.
I am going to question some Hollywood physics here.  At the end of Spiderman 2, Octavius tells Spiderman to drop what essentially amounts to a tiny star into the river in order to extinguish it and prevent it from destroying Manhattan.  Ignoring the problems of properly containing the fusion reaction on earth, getting it to begin in the first place, and all the other problems with fusion as an energy source that scientists are currently trying to sort out, I am curious about only this ending.
As I understand it (and feel free to correct me if I am wrong), fusion works by, at very high temperatures, taking two hydrogen atoms and fusing the nuclei together, creating one helium atom.  There are two ways I can think that submerging a star in water could "put out" the star:

cooling the star to the point that the fusion reactions no longer take place
cutting off the star's supply of fuel (hydrogen)

Since I don't know much about nuclear physics, I'm just curious whether either of these would "extinguish" the star, or whether there is another factor I am not considering.
As a follow up, I am also curious what the consequence of extinguishing the star might be.  would there be a tiny supernova, would the star collapse, or would there be some other kind of death?  You can get an idea of the size of the star from this video.
EDIT As Ali points out in the comments, a star that small probably could not exist at all.  For the sake of discussion, I am amending the question as such:
Imagine the star in question is the mass and size of our Sun, and that somehow, somewhere, there is a body of water large enough to submerge the Sun completely.

A:

Just few more points.

A blob of water few times larger than sun would already be a supergiant.(I'll ignore this in the rest of my answer)
The water will not stay still; it will be attracted by star's gravitational field. This will cause the star's mass to increase.
The water which is falling on the star, even if it's initially freezing cold, will heat up dramatically due to the gravitational potential.
Even if the water lowers the temperature instantly to just few hundred kelvins, which may instantly stop the fusion, after the star begins collapsing the temperature will increase rapidly and fusion will start over again shortly.
Depending on how fast the star enters the cold blob of water, I can consider two possibilities:

rapid sinking: The layers of water closer to the star will evaporate, while the rest of the water droplet! is still liquid. This phase transition and the high pressure following it, will shoot the rest of the water out.
adiabatic sinking: As I said earlier, the water will pour into the star increasing its mass. This will certainly change the star's evolution and death; shifting from white and black dwarfs towards neutron stars and blackholes.

To summarize, I don't think dropping a star in a river can halt its fusion; it will possibly cause either of the above possibilities.

