How can Y-dwarf stars have such a low temperature? A recent article from NASA said they found some stars with temperatures "as cool as the human body."  How is this possible?  Does fusion still occur in these stars?
 A: Y-dwarfs are a subtype of brown dwarfs, which don't produce energy like (or certainly don't produce as much as) normal stars. Brown dwarfs have an upper limit and a lower limit on their masses. Both these limits are informal and approximate. These limits aren't like planets, for which the IAU has an accepted definition, but they're reasonably well-defined. Broadly, bigger stars are hotter, so the smallest brown dwarfs will be the coldest, and it turns out that's really cold, by stellar standards.
The upper limit is the smallest object that fuses hydrogen into helium. Above this limit, the dwarf would shine like a regular star e.g. the Sun. But below this limit, hydrogen will be fused, but not all the way to helium. So a little bit of energy is produced, but relatively little, because the real energy kick comes from the last step of the proton-proton chain, when two 3He atoms fuse into 4He and two protons. So if the core isn't hot enough for this step to happen, some energy is produced, but really not much.
The lower limit is basically when no fusion happens at all. That is, not even the first step of hydrogen fusion (into deuterium) takes place. This limit is less precise, but below it we'd be talking about something more like a big version of Jupiter. And that's cold. Although the brown dwarf may produce a tiny amount of energy through deuterium fusion, most of the surface heat is probably left over heat from when it formed, and it may have had 10 billion years in which to cool.
For reference, keep in mind that the surface temperature of Jupiter, for example, is about 165 K, over 100 K below freezing water. So if you make a big version of it that isn't producing much energy, it isn't crazy that it wouldn't be much hotter. The confusion probably just comes from referring to brown dwarfs as "stars", when they aren't stars of the sort that most people are familiar.
A: From the article you linked

They are too low in mass to fuse atoms at their cores and thus don't burn with the fires that keep stars like our sun shining steadily for billions of years. Instead, these objects cool and fade with time, until what little light they do emit is at infrared wavelengths. 

So, no.

Expanding a little, the temperature of these objects depends the balance between heat inputs (on residual heat of formation, any heat due to radioactive decay in their content, and Virial heating) and radiative cooling. They cool down over time, but the time scales can be very long indeed.
