How to Distinguish between Temperature and Doppler effect using Black-body radiation?
Without any other information, you cannot distinguish between the two effects.  

$$ T = T_0 (1 + z) $$

A blackbody spectrum of temperature $T$ is identical to a blackbody spectrum of temperature $T_0$ with redshift $z$.

For stellar/galactic radiation, we can use the fact that the radiation is not a perfect blackbody.  For the CMB, we can use the fact that atomic combination happens only below a particular temperature.