= Solution
A continuum peak gives a color <temperature> through Wien's law, provided the continuum is approximately Planckian and extinction is corrected. Broad-band colors or a fitted <spectral energy distribution> compare flux ratios with model atmospheres; they require a reddening estimate, abundance and gravity assumptions, and calibrated passbands. Spectroscopic line ratios or excitation/ionization balances provide another <thermometer>, requiring atomic data and a suitable atmosphere model, often <local thermodynamic equilibrium>.
For this cool giant, line blanketing and molecular absorption substantially distort a simple continuum peak, so Wien's law is the least reliable of these approximations. A detailed spectroscopic analysis, checked against a multi-band atmosphere fit, would generally be the strongest of the three if good data and model parameters are available. There is no unconditional accuracy ranking without <Measurement error>[measurement errors] and model systematics; an accurately measured <angular diameter> plus bolometric flux would offer a more direct effective-temperature determination, if obtainable.
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