Simple physical models are often difficult to obtain for nonhomogeneous transport phenomena that involve complex couplings between several distributed variables, such as temperature profiles in tokamak plasmas. Model-based current or combustion control approaches necessitate plasma models with real-time computation capabilities. This may prevent the use of classical knowledge-based physical models and motivates dedicated identification methods to exploit the large available experimental data. Based on distributed temperature measurements, this paper proposes a parameter-dependent identification method that first relates the normalized profiles distribution to a specific shape description thanks to a three-hidden-layers neural network architecture. The amplitude of the profiles is then constrained by the global energy conservation (0D) with an identified time constant. The shape parameters and time constant are related to the global parameters using appropriate scaling laws. Experimental results illustrate the efficiency of the proposed identification method to estimate TORE SUPRA temperature profiles.