Magnetic Resonance Imaging is one of the most prevalent, reliable, and comprehensive thermal monitoring methodology to measure tissue temperature changes during thermal therapies. The proton resonance frequency shift (PRFS) technique is a widely MRI thermal imaging method. However, the PRFS method is sensitive to inter-frame motions that may result in incorrect temperature change profiles. Considering each MRI temperature image as a superposition of a temporally correlated background and a sparse matrix representing motion artifacts, we aim to recover the low-rank matrix from corrupted observations using robust principal component analysis. This problem is solved using iterative soft thresholding of the singular values of both low-rank and sparse matrices and singular value thresholding techniques. We apply this method to MRI observations with artificial introduced motion artifacts and the results indicate that the proposed approach is effective in recovering the clean temperature profiles from noisy observations during heating procedures with average of %81 decrease in RMSE.