Breast cancer is the second most cause of the death among the women in society. Thermography is the non-invasive, non-contact imaging modality that can be used for the early detection of breast cancer. This paper proposes the development of the mathematical model using Penne’s bio-heat transfer equation, and the estimation of the location and the size of the tumour using Metropolis-Hasting (MH) algorithm. This paper also proposes the pre-processing of the thermal images using RGB max filter and Grab-cut algorithm to extract out the region of interest where the probability of the presence of the tumour is more.