Early diagnosis of breast cancer unequivocally improves the survival rate of patients and is crucial for disease treatment. With the current developments in infrared imaging, breast screening using dynamic thermography seems to be a great complementary method for clinical breast examination (CBE) prior to mammography. In this study, we propose a sparse deep convolutional autoencoder model named SPAER to extract low-dimensional deep thermomics to aid breast cancer diagnosis. The model receives multichannel, low-rank, approximated thermal bases as input images. SPAER provides a solution for high-dimensional deep learning features and selects the predominant basis matrix using matrix factorization techniques. The model has been evaluated using five state-of-the-art matrix factorization methods and 208 thermal breast cancer screening cases. The best accuracy was for non-negative matrix factorization (NMF)-SPAER + Clinical and NMF-SPAER for maintaining thermal heterogeneity, leading to finding symptomatic cases with accuracies of 78.2% (74.3–82.5%) and 77.7% (70.9–82.1%), respectively. SPAER showed significant robustness when tested for additive Gaussian noise cases (3–20% noise), evaluated by the signal-to-noise ratio (SNR). The results suggest high performance of SPAER for preserveing thermal heterogeneity, and it can be used as a noninvasive in vivo tool aiding CBE in the early detection of breast cancer.