Stepping back for a moment, a few extra thoughts.
The question is probably too tightly posed. So, ignoring the issues of just what a spacecraft would be doing, and how the internal systems would be designed, what are the heat issues?
That far from the sun things are going to be different from at the Earth’s orbital distance. The sun is a tiny dot in the sky, and planets have liquid methane seas. It is cold. So you might as well just think of it as being close enough to inter-stellar space. The question then becomes: how long could you maintain a livable temperature on a spacecraft buildable with current technology in interstellar space, with no functioning internal energy sources?
This comes down to really three things. How much heat you had on board, how good your thermal insualation is, what your emissivity is.
Heat on board, comes down to mass. If we assume that you had a nice fat spacecraft that was mostly at a human happy temperature, you might have a reasonable amount of heat. Big tank of water would be a nice start. In general of course spacecraft themselves are designed to minimum wieght, so you probably won’t get much help from the craft proper.
Insulation. Since we are in a vacuum, we don’t need to worry about conduction or convection. So it is only a matter of trying to keep the radiated heat in. The answer here is going to be multiple layers of reflective material. A really nice example is the solar shield on the recently launched Hershel telescope, or best of all, the shield on the James Webb Telescope http://www.jwst.nasa.gov/sunshield.html. These are capable of sitting at Earth orbital distances and yet maintaining cryogenic temperatures on the other side. Indeed the temperature extremes are greater than interstellar to here. However the ultimate extremes are dependant upon the evaporation of liquid Helium, so this counts as active cooling. But the principle is sound. The same design could keep a large fraction of the heat inside your spacecraft.
Part of the mechanism by which the sun shields work is low emissivity. They are highly polished, and emit vastly less energy than a matt or a black surface. The outermost surface of the shield is what radiates the heat out into space where it is lost. So its emissivity is the final determinant of heat loss.
So, the answer? Hard to say. My expectation is that you will still freeze. Especially if the scenario was one where the loss of heating was unexpected. But would it be possible to design a spacecraft with modern, existing, technology that could survive? Very likey. But it would not be trivial. Live humans create some heat. But enough? Hard to say.
For completeness, the issues with heat and heat rejection are almost backwards at Earth - Sun distances. At interstellar distances a black surface will become cold very quickly, and a polished silver one will lose heat much slower. Nearer the sun, the black body will absorb solar radiation quickly and heat up dramatically, whereas the polished one will adsorb much less. The matt white of the Shuttle and spacesuits turns out to be a bit of a happy medium, and stabilises at a temperature that is within the bounds of the suit or spacecraft’s systems to be able to keep the interior within habitable bounds. A suit for visiting Venus would be silver, a suit for Mars probably black, and a suit for visiting Titan silver again. Roughly.