  By relating the charge multiplicity distribution and the temperature of a
de-exciting nucleus through a deep neural network, we propose that the charge
multiplicity distribution can be used as a thermometer of heavy-ion collisions.
Based on an isospin-dependent quantum molecular dynamics model, we study the
caloric curve of reaction $^{103}$Pd + $^9$Be with the apparent temperature
determined through the charge multiplicity distribution. The caloric curve
shows a characteristic signature of nuclear liquid-gas phase transition around
the apparent temperature $T_{\rm ap}$ $=$ $6.4~\rm MeV$, which is consistent
with that through a traditional heavy-ion collision thermometer, and indicates
the viability of determining the temperature in heavy-ion collisions with
multiplicity distribution.

Nuclear Theory;High Energy Physics - Phenomenology;Nuclear Experiment