Theoretical and experimental study of shape of the Arai-Nagata diagrams for the natural remanent magnetization (NRM) consisting of two low- and high-temperature partial thermal remanent magnetization vectors directed at angle $theta$ to each other is considered. Assuming that the NRM is carried by single-domain and/or small pseudosingle-domain grains, that is, the Thellier laws of additivity and independence are valid, a theoretical consideration showed that the low-temperature portion of the diagram has a hyperbolic shape. A striking feature of the diagram is that at obtuse angle $theta$ and strong enough low-temperature component it exhibits a minimum. The theoretical conclusions were examined experimentally; the results of the experiments are in a good agreement with the theoretical predictions. The shape of the low-temperature portion is predetermined by the angle $theta$, the relative intensity of low-temperature component, and the field h in which this component was imparted. These three parameters can be found from the results of Thellier experiments by the least squares method. It opens a way to determine the paleofield h and the angle $theta$ which are characteristics of the low-temperature (presumably secondary) remanent magnetization. A few examples of such the determinations on samples from Proterozoic collections are reported.