This is a hard question to answer for any particular star except perhaps the Sun. The Sun's core temperature is about 15 million degrees Kelvin. For stars that are 10 times less massive than the Sun, this temperature dips to nearly 1 million degrees, while stars that are about to go supernova, the temperatures can be as high as 2 billion degrees. Very roughly, a formula for core temperature is:

    T   =  6 million x mass/radius  K

where mass is in multiples of the Sun's mass and radius is in multiples of the Sun's radius.

Alpha Centauri is a sun-like star and probably has the same core temperature as well. Vega and Sirius are about 3 times the mass of the Sun and slightly larger in radius so they probably are about twice the core temperature of the Sun. This relation doesn't work for red giants or supergiants because the core is not supported by pressure from hot gas, but from something called 'electron degeneracy pressure'.