  We show that a gas thermometer in contact with a stationary classical system
out of thermal (Boltzmann) equilibrium evolves, under very general conditions,
towards a state characterized by a Levy velocity distribution. Our approach is
based on a kinetic-like equation that applies to a wide class of models for the
system-thermometer interaction. The results clarify the role of non-exponential
energy distributions as possible generalizations of the Boltzmann distribution
for systems where the usual formulation of thermostatistics may not apply. In
particular, they show that the power-law distributions derived from Tsallis's
nonextensive formalism are irrelevant to the stationary state of the
thermometer, thus failing to give a consistent description of the
system-thermometer equilibrium. We point out the need of a generalized
thermostatistical formulation able to give a unified frame to Levy and Maxwell
distributions.
