 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 errors and model systematics; an accurately measured angular diameter plus bolometric flux would offer a more direct effective-temperature determination, if obtainable.