This paper presents a method to reveal the channel temperature profile of high electron mobility transistors (HEMTs) in a multi-stage monolithic microwave integrated circuit (MMIC). The device used for this study is a two-stage Xband low-noise amplifier fabricated using 0.15 µm GaN-on-SiC technology with 4x50 µm and 4x75 µm HEMTs at the first and the second stage, respectively. The surface temperature measured through infrared (IR) thermography has a diffraction-limited resolution. Moreover, it is impossible to measure sub-surface Tmax residing inside the two-dimensional electron gas of HEMT using IR thermographic measurements. Finite element analysis (FEA) thermal simulations are performed in this study to acquire the surface and sub-surface temperature profiles of the whole MMIC. IR measurements and FEA simulations are integrated through a correlation-based method verifying the accuracy of the FEA-based temperature profiles. This method leads to accurately finding the hotspots in the MMIC, thus revealing the Tmax of both stages. The correlation method using two filters approach to match the measurements and simulated temperature profiles of all the stages finds its application in MMICs' high-temperature operating lifetime reliability tests.