It's been done before, and it can done again. They say good artists borrow, and great artists steal, so it's time to nick the answer from someone who's already used it to cool down the Sun. I refer, of course, to the movie Sunshine (2007) which postulated q-balls would be responsible for shutting down the Sun.
The concept wasn't used explicitly in the movie, that is, no-one explained this was going on inside the Sun, but the concept was devised by physicist Brian Cox, the movie's science consultant.
Cox reasoned as follows in setting up the basic rationale about why the Sun might cool down and the physics of dark matter that might permit the existence of q-balls.
The Sun will not live forever. It has enough fuel left, if our current understanding is correct, for another 5 billion years, at which point it will die. But could it be possible for the Sun to die much sooner, within the next 100 years even? From a scientific perspective, it should be said that this is very unlikely. But, it is also true that there is a lot about the universe that we do not understand.
Over the last few years astronomers have observed that there is extra
"stuff" in the universe that we can see only by its gravitational
influence on stars and galaxies. This stuff goes by the name of Dark
Matter, and there is five times as much Dark Matter in the universe as
there is normal matter, the stuff that makes up you, me, and the stars
and planets we can see with our telescopes. What is this mysterious
stuff? It's possible, some scientists would say likely even, that this
stuff is made of particles known as supersymmetric particles, a new
and exotic form of matter that is high on the list of potential
discoveries at CERN's giant Large Hadron Collider, a 27km in
circumference machine which begins operations this year after almost a
decade of construction.
Once the possibility of dark matter in the form of supersymmetric particles has been established, he reasoned how q-balls might influence the Sun and cause it to cool down.
Theoretical physicists have spent many years calculating the properties of these supersymmetric particles, and we have a reasonable theoretical understanding of how they might behave. One possibility is that they could clump together into giant balls known as Q-balls. If this is true, then these heavy and exotic objects could have been made billionths of a second after our Universe began, and still be roaming the Universe today. It is speculated that, if a Q-ball drifts into the heart of a super-dense object such as a neutron star, it could begin to eat away at it's [sic] core like a cancer, until the star is no longer massive enough to maintain itself and explodes in a violent explosion. Such explosions, known as gamma ray bursts, are seen in the Universe, although their cause is as yet unknown.
Could such a dangerous, exotic object drift into the Sun's core and
cause it to stop shining? It is likely that the Sun is many times too
diffuse to stop a Q-ball - it would power right through. But maybe,
just maybe, some strange exotic form of matter from the earliest times
in the universe could settle deep within the Sun's core, and disrupt
its function enough to cause the catastrophic scenario seen in
Sunshine. It's far-fetched, but we have a saying in physics that
anything that isn't explicitly ruled out is therefore possible, so in
the final analysis, you never quite know.
While the physics is a bit iffy, but that's not a problem for science-fiction, the q-ball concept is plausible in terms of current physics. Also, as Brian Cox points out, this scenario does explain some natural phenomena we do observe in the universe.
Also, not discussed by Brian Cox, is the fact that it takes roughly one million years for the energy produced at the centre of the Sun to migrate to its surface. This suggests that, if the Sun was cooled by a q-ball, that the q-ball would have entered the Sun about one million years ago.
EDIT 2016-October-09:
Because Citizen JDlugosz requested additional information about the q-ball's mechanism further research has been undertaken by your humble interlocutor. A full discussion can be found here, but its arguments will be laid out in the following.
While the story might recall the asteroid-detonating plot of Michael Bay’s Armageddon (1998), the mission aboard Icarus 2 is far more complex: Here, the astronauts aim to destroy a supersymmetric particle called a Q-Ball that is eating the Sun from the inside out.
First posited some 20 years ago by Harvard physicist Sidney Coleman, a
Q-Ball is a super-heavy object that could have formed during the Big
Bang and would have the ability to break down ordinary matter made of
protons and neutrons. Normally, protons are stable because they are
the lightest particles to carry a conserved quantum number called the
baryon number, and there is no way for them to get rid of this number
and decay. But Q-balls, made from tightly packed supersymmetric
particles that can accommodate a baryon number at lesser energetic
cost than a proton, allow the proton to disintegrate, while the baryon
number of the Q-ball increases. Q-Balls, says Dr. Cox, "can be
pictured as giant agglomerations of supersymmetric particles that
could, if they drifted into the heart of a star, eat away like a
cancer, eventually destroying the star from within."
Because q-balls are highly speculative entities, there are objections from other physicists about their feasibility, and as Sun-stoppers.
But there are several major problems on which this premise rests, not least of which is that supersymmetry and Q-Balls are as yet completely unproven. Even Cox admits that our sun is not dense enough to hold a hypothetical Q-Ball. Because the supersymmetric Q-ball is a very compact assembly of heavy particles packed in a small volume, it is billions of times denser than an atomic nucleus, so it would fly right through the sun "like a knife through whip cream," says UCLA physicist Alexander Kusenko, one of the leading Q-Ball researchers. Kusenko theorizes that a more likely target for a Q-Ball is a neutron star, which is far denser than the sun.
But for argument's sake, even if a Q-Ball did invade the sun and
started eating the solar matter, New York University's Georgi Dvali,
co-author with Kusenko and Mikhail Shaposhnikov of the paper "New
Physics in a Nutshell, or Q-ball as a Power Plant," says the energy
released by this process would be so high that "the intensity of the
sun's radiation should increase enormously." He adds, "So then the
problem of our civilization will not be the sun's death, but rather
enormous radiation before it."
As Kusenko says, "You would not be freezing, you would be fried."
Actually Brian Cox acknowledged that neutron stars were more likely to stop a q-ball and then have gnarl out their internal matter until their gravitation was reduced to a level where the neutron star could no longer hold itself together and end in a vast explosion. However, even if the exotic matter was present in our Sun to make a q-ball stop and damp down thermonuclear reactions, this might not stop Earth from being fried as the Sun passed through its red giant phase prematurely before it could cool down.
UCLA professor of solar physics Roger Ulrich doubts that humankind would even be around if the Earth got to a point where it was freezing over. By that point, as he sees it, the sun would have already passed through the red giant phase into a cooling white dwarf. "Well before the sun makes it too cold for us, we are going to get seriously roasted and quite possibly the whole earth could be evaporated and incorporated into the solar gas," he says.
In summary, the q-ball can only be regarded as a plausible mechanism for cooling a star if certain ad hoc assumptions are made. This is a typical dilemma when scientific concepts are imported into science-fiction to make its fantastic content seem realistic or naturalistic. The science itself often has to be stretched and bent to fit the fictional circumstances; quite enough out of, and, in many case, well beyond what many scientists would consider reasonable deviations from scientific possibility.