Why is Rosetta's Comet so "warm"? Rosetta Comet AKA 67P/Churyumov–Gerasimenko has the surface temperature range of -43 to -93 degree Celsius. 

Now, if we compare that with the Mercury (I chose Mercury cause it's closest to the Sun and has the thinnest atmosphere), the minimum surface temperature is -170 degrees Celsius. A little farther from that, on Earth's Moon, while at night, the temperature can drop up to -233 degree Celsius.

Rosetta's Comet is farther from the Sun as compared to both objects (Perihelion 1.2432 AU, Aphelion 5.6829 AU); however, a lot warmer. Why is that?
67P/Churyumov–Gerasimenko is actually not really warm when compared to these bodies.
You quoted figures for the minimum temperatures for Mercury and the Moon. Those are accurate but misleading. Both are for nighttime temperatures, taken from locations on the bodies that are facing away from the Sun. Daytime temperatures can skyrocket, to 427 degrees Celsius during the day on Mercury. The Moon can also get very hot during the day, although nowhere near as hot as on Mercury,
Looking at it like this, 67P/Churyumov–Gerasimenko's surface temperatures are pretty moderate, and nowhere near extreme. Rubin et al. (2015) suggest that it formed in extremely cold conditions - albeit ones not too extreme, for a comet.
The ESA has something related to say on the matter:

At these distances, the comet covered only a few pixels in the field of view and so it was not possible to determine the temperatures of individual features. But, using the sensor to collect infrared light emitted by the whole comet, scientists determined that its average surface temperature is about –70° Celsius.
The comet was roughly 555 million km from the Sun at the time — more than three times further away than Earth, meaning that sunlight is only about a tenth as bright.
Although –70° C may seem rather cold, it is some 20–30° C warmer than predicted for a comet at that distance covered exclusively in ice.

That said, evidence from the mission has made scientists think that an surface with a lot of dust may be the norm for comets.
67P/Churyumov–Gerasimenko isn't warmer or colder than the other bodies at this distance from the Sun. It's simply milder.

I would wager that the reason Mercury and the Moon can get so cold is because they don't really have atmospheres. Over the course of a day, Earth's atmosphere heats up a bit, and over night, it retains that heat, meaning that the surface can stay relatively warm. Mercury's atmosphere is extremely tenuous. The same goes for the Moon.
This might not be an issue, but one day on Mercury lasts 59 Earth days. One day on the Moon lasts for about one Earth month. This means that while there's time to trap some heat, there's also the same amount of time to lose it, and without an atmosphere, the heat gained is soon be lost.
67P/Churyumov–Gerasimenko also doesn't have an atmosphere to speak of, but it rotates quickly - rotating once every ~12.5 hours. This isn't necessarily perpendicular to the orbital plane, so not every part of it will face the Sun during a rotation, but it does mean that there's not as much time to lose heat.