For a star similar to the Sun, what critical temperature must the core reach to initiate sustained nuclear fusion?

About 15 million Kelvin

The true birth of a star, marking the transition from a gravitational contracting object to a stable stellar body, occurs only when the temperature and pressure in the core reach a specific threshold necessary to ignite sustained nuclear fusion. For a star comparable in mass to our Sun, this critical temperature is approximately 15 million Kelvin. At this extreme heat and density, the electrostatic repulsion between the positively charged hydrogen nuclei is overcome, allowing them to fuse together, predominantly forming helium and releasing massive amounts of energy. This resulting outward pressure perfectly balances the inward force of gravity, achieving hydrostatic equilibrium and settling the star onto the main sequence.