  It is shown that the Unruh effect, i.e. the increase in temperature indicated
by a uniformly accelerated thermometer in an inertial vacuum state of a quantum
field, cannot be interpreted as the result of an exchange of heat with a
surrounding gas. Since the vacuum is spatially homogeneous in the accelerated
system its temperature must be zero everywhere as a consequence of Tolman's
law. In fact, the increase of temperature of accelerated thermometers is due to
systematic quantum effects induced by the local coupling between the
thermometer and the vacuum. This coupling inevitably creates excitations of the
vacuum which transfer energy to the thermometer, gained by the acceleration,
and thereby affect its readings. The temperature of the vacuum, however,
remains to be zero for arbitrary accelerations.
