I think you're mixing up spectral temperature with effective temperature. Effective temperature is about total power (per the Stefan Boltzmann law), not about

I think you're mixing up spectral temperature with effective temperature. Effective temperature is about total power (per the Stefan Boltzmann law), not about the color of the light (per Wien's law). Compare https://en.wikipedia.org/wiki/Effective_temperature https://en.wikipedia.org/wiki/Effective_temperature with https://en.wikipedia.org/wiki/Color_temperature https://en.wikipedia.org/wiki/Color_temperature