  Single-qubit thermometry presents the simplest tool to measure the
temperature of thermal baths with reduced invasivity. At thermal equilibrium,
the temperature uncertainty is linked to the heat capacity of the qubit,
however the best precision is achieved outside equilibrium condition. Here, we
discuss a way to generalize this relation in a non-equilibrium regime, taking
into account purely quantum effects such as coherence. We support our findings
with an experimental photonic simulation.
