  The measurement and control of the temperature in microscopic systems, which
are increasingly required in diverse applications, are fundamentally important.
Yet, the measurement of the three-dimensional (3D) temperature distribution in
microscopic systems has not been demonstrated. Here, we propose and
experimentally demonstrate the measurement of the 3D temperature distribution
by exploiting the temperature dependency of the refractive index (RI).
Measurement of the RI distribution of water makes it possible to quantitatively
obtain its 3D temperature distribution above a glass substrate coated with gold
nanorods with sub-micrometer resolution, in a temperature range of 100C and
with a sensitivity of 2.88C. The 3D temperature distributions that are obtained
enable various thermodynamic properties including the maximum temperature, heat
flux, and thermal conductivity to be extracted and analyzed quantitatively.
