Donuel,

About 10-20 degrees Kelvin. And the cloud heats up by two processes, as it collapses under its own gravity, potential energy is converted to kinetic energy (energy of motion), and then to thermal energy, and to start with the energy is radiated away, but then the density increases and the cloud heats up, and when it has heated up enough nuclear fusion stars, and it becomes a star.

Complicating all this are things like turbulence and magnetism, which result in scary equations which can really only be solved by big, fierce computers. Here my knowledge runs out.

As to whether stars can form outside a galaxy, that may be so, and probably must have been so in the distant past, but as far as I know its not been observed. Its quite difficult to do so, due to us living in the middle of one, regions outside galaxies are far away and often obscured.