Hydrodynamic models of the Sun allow one method of estimating its internal properties. To do this, the Mass, radius, surface temperature, and total luminosity (radiative energy emitted)/s of the Sun must be known (determined observationally). Making several assumptions, e.g., that the Sun behaves as a fluid and that local thermodynamic equilibrium applies, the stellar equations of state can be used. Numerical methods are applied to these equations to determine the internal properties of the Sun, such as its central temperature.
A great example for how to work this problem your self can be found in the undergraduate text, 'An Introduction to Modern Astrophysics' by Carroll and Ostlie (Section 10.5). The FORTRAN code to run your own stellar model is included in Appendix H.
A comprehensive review paper on how stars of different masses evolve internally (e.g., with respect to T, P, etc.) that is worth reading is:
http://adsabs.harvard.edu/abs/1967ARA%26A...5..571I
A very interesting historical overview of the development of the Standard Solar Model:
http://arxiv.org/abs/astro-ph/0209080
This (admittedly dry) paper gives you a good idea of how well the 'standard' solar models estimate the internal properties of the Sun using helioseismology and neutrino measurements to help tie down their boundary conditions:
http://adsabs.harvard.edu/abs/1997PhRvL..78..171B
The answer is that they match incredibly well (>0.2% error)
These were the least technical (but still academically published) references I could find.
Here is a comprehensive page on the state-of-the-art in solar modelling and measuring the internal Sun using Helioseismology:
http://www.sns.ias.edu/~jnb/Papers/Preprints/solarmodels.html
(highly technical)
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