If I understand the thinking, the notion is of a photon gas which is isotropic in a particular "rest" frame. Within this gas, the moving ship sees an anisotropy -- blue-shifted high energy forward and red shifted low energy aft.So, the doppler effect will make the ship
- get (to the occupants) and appear (to a stationary observer) as being hotter at the front and colder at the rear...
while time dilation makes the ship
- get hotter while appearing colder, both all 'round.
That's fine, I've just never heard of doppler shift being referred to as a temperature alteration. E.G., we don't say redshifted stars/galaxies are colder than blueshifted ones, do we?Again, this depends. If you mean the rest temperature, sure. If you mean the temperature that you would associate with the spectrum radiated from the body that will be affected by the Doppler effect and correspondingly red or blue shifted.