We consider quantum fields around uniformly accelerated black holes in
the eternal Ernst geometry. At a particular value of the acceleration
, the Bogoliubov transformation, which would be responsible for the la
te-time Hawking radiation, is found to be trivial. When this happens,
Hawking's thermal radiation, Doppler shifted or not, is absent to the
asymptotic inertial observers despite the nonzero Hawking temperature,
while the comoving observers find the black hole radiance exactly bal
anced by the acceleration heat bath. We close with a few comments.