  Almost a century ago, Johnson and Nyquist presented evidence of fluctuating
electrical current and the governing fluctuation dissipation theorem (FDT).
Whether, likewise, temperature T can fluctuate is a controversial topic and has
led to scientific debates for several decades. To resolve this issue, there was
an experiment initially in 1992 where the authors found good agreement between
the FDT theory for heat and experiment on a macroscopic sample. A key question
is what happens when we consider a nanoscale system with much fewer particles
at 100 times lower temperatures. This challenge has not been addressed up to
now, due to the demanding experimental requirement on fast and sensitive
thermometry on a mesoscopic absorber. Here we observe equilibrium fluctuations
of temperature in a canonical system of about 10^8 electrons exchanging energy
with phonon bath at a fixed temperature. Moreover, temperature fluctuations
under nonequilibrium conditions present a nontrivial dependence on the chemical
potential bias of a hot electron source. These fundamental fluctuations of T
set the ultimate lower bound of the energy resolution of a calorimeter.
