Infrared thermography has been seen as an effective screening modality for detecting breast cancer as it identifies even very small tumours and hence leads to early diagnosis. It is non-invasive, safe, and painless that brings valuable information about the location of malignant substances. The application of deep learning algorithms in thermography is found to increase the accuracy of detection. This paper proposes an automated and optimised convolution neural network-based system for tumour segmentation of the breast thermogram images. Moreover, it is optimised with a recent bio-inspired optimisation called the mayfly algorithm. The optimisation techniques sometimes trap local optima, attain premature convergence, and cannot trade-off between the exploration and exploitation phase. In the proposed work, these problems can be overcome through an inertia weight updation policy. The effectiveness of the suggested approach has experimented on publicly accessible thermal image breast cancer datasets. The results proved that this technique can be helpful for physicians to make better decisions on breast cancer diagnosis.