This work includes a brief overview of the applications of the powerful and easy-to-perform method of microwave radiometry (MWR) for the diagnosis of various diseases. The main goal of this paper is to develop a method for diagnosing breast oncology based on machine learning algorithms using thermometric data, both real medical measurements and simulation results of MWR examinations. The dataset includes distributions of deep and skin temperatures calculated in numerical models of the dynamics of thermal and radiation fields inside biological tissue. The constructed combined dataset allows us to explore the limits of applicability of the MWR method for detecting weak tumors. We use convolutional neural networks and classic machine learning algorithms (k-nearest neighbors, naive Bayes classifier, support vector machine) to classify data. The construction of Kohonen self-organizing maps to explore the structure of our combined dataset demonstrated differences between the temperatures of patients with positive and negative diagnoses. Our analysis shows that the MWR can detect tumors with a radius of up to 0.5 cm if they are at the stage of rapid growth, when the tumor volume doubling occurs in approximately 100 days or less. The use of convolutional neural networks for MWR provides both high sensitivity (sens=0.86) and specificity (spec=0.82), which is an advantage over other methods for diagnosing breast cancer. A new modified scheme for medical measurements of IR temperature and brightness temperature is proposed for a larger number of points in the breast compared to the classical scheme. This approach can increase the effectiveness and sensitivity of diagnostics by several percent.