How hot must a star get before it actually becomes a star? Why does it need to get so hot? Please find an official site to quote from, if you can.
Star temperature is an interesting question since temperature varies a lot in a star. I think that the more relevant temperature to this question is the core temperature of the star: a star is born when it starts to burn hydrodgen in its core.
(See this Wikipedia page)
The temperature needed for hydrodgen burning is 10 million Kelvin, so that's how hot a star must be to be considered as a star. It needs to get so hot, because else it will fail to burn hydrodgen and will become a "failed star": a brown dwarf.
Surface temperature can be misleading, since the temperature ranges in which lay stars are not populated only by stars, but also by other objects such as hot Jupiters, with surface temperature ranging from 1000 to 3000 K.
From a physics perspective
From a physics perspective an object is a star when it is undergoing nuclear fusion, generally of hydrogen atoms at its core, this is regardless of its temperature!
A star is not determined by its temperature, it is instead determined by it's internal processes.
This does mean that if Jupiter began nuclear fusion it would be considered a star, albeit a minuscule one.
In this case it is a yes/no distinction of if an object is a star.
From an observational point of view once something is classified as a star there are 7 groups it can fall in to determined by its features.
Sourced From: http://en.wikipedia.org/wiki/Star#Classification
Note: Three more classifications L T and Y have been added to the colder end of this list, but I am unsure of the cut off points so omitted them.
But strangely they are not classified by temperature but by their spectrum, it just so happens that their spectrum correlates to their temperature! The temperature spoken of here is of the photosphere of the star (where the photons begin free streaming), not its core (where photons are created from ongoing fusion reactions).
Dwarf stars have their own classification system prefixed by the letter D though.
Quote from Wiki article: