  We model the situation in which a photon detector moves with constant
velocity in a Minkowski heat-bath by considering an Unruh-DeWitt detector, with
variable energy gap $\hbar \omega$, moving on a brane, at a non-zero (Unruh)
temperature $T$ due to acceleration in an orthogonal direction. We compute the
angular response for a 2-brane. At low velocity we find agreement with the
standard Doppler shift formula in the limit $\hbar\omega \gg T$ in which the
photon gas is classical; otherwise there is a discrepancy, which we attribute
to angular-dependence of the induced emission rate. At relativistic velocities
our result disagrees with the standard formula even when $\hbar\omega \gg T$,
and above a critical velocity there is no response from the detector within a
`backward' cone. We discuss potential implications for observations of the
cosmic microwave background radiation.
