I've just learned about redshift a couple of days ago, and i found myself questioning why relative motion to the observer is the only thing that could affect the intensity of the red shift of the frequencies of electromagnetic waves. Can't temperature cause blue shift as photons are more energetic causing them to oscillate more (higher frequencies)? My second question regarding this topic is: can distant galaxy that appears to be moving away have no red shift due to its average temperatures being very high?
Temperature is connected to the microscopic motion of a system. "Higher temperature" photons are, averagely, more energetic, but this is not related to the Doppler shift. I try to explain better:
Consider a body with a lower temperature T1 (e.g. 300K), and a body with a higher temperature T2 (e.g. 500K), both at rest. These two bodies will emit thermal radiation and the two spectra will be slightly different, because in the second case (500K) there will be more photons at high frequencies than in the first case (300K), but this is due only to the two bodies emitting different amount of energy.
Now consider two bodies at the same temperature, but one is at rest with respect to the observer whereas the other one is moving. In this case, even if the temperature are the same, the spectra will be different due to that relative motion. This is the Doppler effect (or shift): the frequencies (and so the spectrum) of the photons are shifted because of the motion of the source.
Now, temperature can actually cause. Doppler shifts. Consider a gas of atoms. At higher temperature the atoms will move (with respect to the observer) faster; but doppler shifts happen when a source is moving, and the shifts depend on relative velocity. So, a hotter gas will cause positive and negative shifts higher than those of a cooler gas. However this effect is usually small in comparison with other effect, so the gases' spectra you will see will be essentially the same (the fact that a body with a given temperature emit thermal radiation, according to Stefan-Boltzmann law and Vien's law is not related to Doppler effect).