We're pretty much certain that dark matter exists, but we're still working to nail down precisely what dark matter is. One leading candidate, known as the WIMP, might be trapped inside the Sun, sucking heat away and altering fusion reactions.
If WIMPs - weakly interacting massive particles - really are the missing dark matter particles, then some of them are being sucked into the Sun by our star's intense gravity. Once inside, the WIMPs would gain energy by smashing into protons, which would very slowly move heat away from the center of the Sun. The effect should be noticeable - we should be able to detect WIMP-altered solar temperatures.
Unfortunately, we can't stick a thermometer into the Sun and take a measurement, or even do the less fanciful version of that. We're stuck with indirect methods, and the most promising is to check on the neutrinos that the Sun is emitting. The neutrinos are created by various fusion reactions inside the Sun, and different reactions occur at different locations along the solar radius. We know a reaction producing boron-8 occurs very near the center of the Sun, on about 4% of the solar radius, while nitrogen-13 is produced further out, at about 16% the solar radius.
Those reactions vary with the temperature of the Sun at their point along the solar radius, so any solar dark matter would leave a very noticeable signature as it affected these fusions. All we would then have to do is check the neutrino fluxes emanating from the Sun to see if there are any signs of change. It should be pretty noticeable - simulations by physicists Ilidio Lopes and Joseph Silk suggest the presence of WIMPs would alter the amount of neutrionos created in boron-8 reactions by a whopping 30%.
The two physicists believe that, if they're right, the dark matter might actually be directly detectable on more powerful neutrino sensors, perhaps even within the bounds of what we can do with upgrades to existing devices. Gianpaolo Bellini, a scientist at Italy's Borexino solar-neutrino detector, points out that current solar neutrino measurements don't bear out their hypothesis, although he concedes that there's a big enough margin for error with their detectors that they can't rule out Lopes and Silk's ideas.
There's also a more subtle problem. This new theory depends on us having a pretty clear idea of the Sun's internal mechanisms and workings, so that we can definitively say that WIMPs are causing any alterations and not something naturally occurring within the Sun. That's knowledge we simply don't possess yet, although Lopes and Silk are optimistic that, if nothing else, their theory can help narrow down the possible candidates for the dark matter particle.