At what temperature does a stars core begin its function reaction

100 million degrees.

100 million degrees should be your answer...

radiative zone

explanation    

radiative zone is the layer of the sun which energy is transferred away from the core by radiation. although, the core is the only part of the sun that produces an appreciable amount of heat through fusion. in fact, 99% of the energy produced by the sun takes place within 24% of the sun's radius.