Macroscopic concepts pertaining to the Unruh effect are elaborated and used to clarify its physical manifestations. Based on a description of the motion of accelerated, spatially extended laboratories in Minkowski space in terms of Poincar\'e transformations, it is shown that, from a macroscopic perspective, an accelerated observer will not register with his measuring instruments any global thermal effects of acceleration in the inertial (Minkowskian) vacuum state. This result is not in conflict with the well-known fact that microscopic probes respond non-trivially to acceleration if coupled to the vacuum. But it implies that this response cannot be interpreted as the effect of some heat bath surrounding the observer. It is also shown that genuine equilibrium states in a uniformly accelerated laboratory are not spatially homogeneous. In particular, all equilibrium states coincide with the inertial vacuum at sufficiently large distances from the horizon of the observer and consequently have the same (zero) temperature there. The analysis is carried out in the theory of a free massless scalar field, but its conclusions hold more generally.