  The existence of fluctuations of temperature has been a somewhat
controversial topic in thermodynamics but nowadays it is recognized that they
must be taken into account in small, finite systems. Although for
nonequilibrium steady states superstatistics is becoming the \textit{de facto}
framework for expressing such temperature fluctuations, some recent results put
into question the idea of temperature as a phase space observable. In this work
we present and explore the statistics that describes a part of an isolated
system, small enough to have well-defined uncertainties in energy and
temperature, but lacking a superstatistical description. These results motivate
the use of the so-called fundamental temperature as an observable and may be
relevant for the statistical description of small systems in physical
chemistry.
