Measurement and control of the temperature in microscopic systems are fundamentally important in science and engineering, with increasing number of diverse applications, including photothermal therapy, inhibition of neural activity, drug delivery, and micro fluidics. Yet, measurement of three-dimensional (3D) temperature distribution in microscopic systems has not been demonstrated. Previous approaches, such as infrared radiometry, fluorescent thermometers and quantitative phase microscopy, measures only 2D distributions with complicated assumptions. Here, we propose and experimentally demonstrate the measurements of 3D temperature distribution by exploiting temperature dependency of refractive index (RI). By measuring RI distribution, 3D temperature distributions of water above a glass substrate coated with gold nanorods are quantitatively obtained with temperature range and sensitivity of $100^\circ C$ and $2.88^\circ C$, respectively. From the obtained 3D temperature distributions, various physical and thermodynamic properties including the maximum temperature, heat flux density and thermal conductivity are extracted and analyzed quantitatively.