  We present a technique based on high resolution imaging to measure the
absolute temperature and the heating rate of a single ion trapped at the focus
of a deep parabolic mirror. We collect the fluorescence light scattered by the
ion during laser cooling and image it onto a camera. Accounting for the size of
the point-spread function and the magnification of the imaging system, we
determine the spatial extent of the ion, from which we infer the mean phonon
occupation number in the trap. Repeating such measurements and varying the
power or the detuning of the cooling laser, we determine the anomalous heating
rate. In contrast to other established schemes for measuring the heating rate,
one does not have to switch off the cooling but the ion is always maintained in
a state of thermal equilibrium at temperatures close to the Doppler limit.
