Flame temperature for cooking food
Blue flame has a hotter temperature. In physics there is a relationship called Wien's displacement law, which states
$$\lambda_{max}T=2.898$$
where $\lambda_{max}$ is the peak wavelength of light emitted (which is the wavelength you see) and T is temperature in kelvins. 

This relationship can be rewritten $$T=\frac{2.898}{\lambda_{max}}$$, or just $T\propto \frac 1 \lambda$. 

From a table we find that the wavelength of blue light is about 450-500 nm and yellow light is 570-590 nm. Since temperature is inversely proportional to wavelength, the light with the smaller wavelength has the higher temperature.

(Now you might quibble that Wien's law is for idealized blackbodies but it can be used to model most things which emit light because of their temperature regardless.)