Red Stars Versus Blue Stars

That's correct Nihar. The color of a star primarily depends on its temperature. The wavelength of the star is given by Wien's displacement law .

$\lambda_{max} = \frac{k}{T}$

It states that the wavelength of the star's light is inversely proportional to the star's surface temperature. Since blue has a smaller wavelength than red, we conclude blue stars are hotter than red stars.

Doppler effect affects the observed wavelength too, but only very slightly, since the radial velocities of stars is very small compared to speed of light.

Let's consider a blue star whose $\lambda \approx 450$ nm. Suppose it is moving away from us with velocity $10$ km/s. The observed wavelength $\lambda_o$ is given by

$\frac{\lambda_o - \lambda}{\lambda} = \frac{v_{star}}{c}$

Since speed of star is very less compared to speed of light, $\lambda_o$ is almost equal to $\lambda$ and Doppler effect does not contribute much to the color of the star.

That's right (+1)!!!