reverse-engineering the temperature derivative

I spent time on the phone with Teresa Huang (NYU) and Soledad Villar (NYU) trying to work out whether we have a good estimate of the derivative of the temperature with respect to spectral shape for stars in SDSS-IV APOGEE data. What we did is we took a ball of synthetic spectra (theory-generated spectra) in the vicinity of the target spectrum, and then regressed against temperature to figure out how the theoretical best-fit temperature ought to depend on spectral shape or spectral features. That's good, but now how do we validate that we got the right answer? We are trying to avoid learning any actual stellar physics here.