Accurate surface temperature prediction is essential for the lifetime and efficiency of a rocket engine. The new ambition of future reusable engines requires perfect knowledge of the thermal environment encountered. In the design phase of such systems and to improve numerical simulations, more resolved experimental data are needed. Experiments are thus conducted by Lab. EM2C, ONERA, CNES, and ArianeGroup on the cryotechnic test bench MASCOTTE operated by ONERA. Conditions representative of those encountered in the gas generator of a rocket engine are investigated. Among them is the cryogenic injection of transcritical methane and oxygen at a very low mixture ratio (0.3) and high pressure (up to 60 bar) through a single coaxial injection element. The present work aims at characterizing the temperature of several surfaces of the combustion chamber in a series of hot fire tests performed in the transient thermal regime and in a short period of time (30 s). For this purpose, dynamic Laser Induced Phosphorescence (LIP) is implemented with the Full Spectrum Fitting method (FSF method), a dedicated approach developed by Lab. EM2C. Single-shot measurements are performed to simultaneously track the temperature of five surfaces at 10 Hz located near and downstream of the flame with a 30 K uncertainty. Data indicate that the temperature peak at ignition can be recorded with LIP measurements in contrast to conventional sensors. The analysis of gas and surface temperatures shows that convection is the predominant heat transfer mode and drives the surface temperature. Thanks to LIP thermometry on the internal and external faces of one of the silica windows, a 1D semi-infinite medium model is applied, showing excellent agreement with the measurements. Fitting this model on the measurements allows the estimation of the local convection coefficient and the prediction of the temperature at any depth inside the walls.