coolest star
The coolest true stars are thought to have surface temperatures around 2,600 K. One example of such a star is Gliese 105C, imaged by the Hubble Space Telescope in 1995.
The main factor determining a star's surface temperature is its mass. Theory puts the lower mass limit for a star at 8% the Sun's mass. Below this limit, it is impossible for the centre of a clump of gas contracting under gravity to heat up sufficiently for spontaneous nuclear fusion to start and maintain itself. Potential stars that fail because their mass is below this limit are called brown dwarfs. Gliese 105C appears to be a true low-mass star, and not a brown dwarf. Its mass is put at 8-9% of the Sun's. Gliese 105C is the binary companion of larger star, Gliese 105A, also known as HD 16160.