The experimental studies on the thermal properties and decomposition course of a novel class of potential anticancer drugs (1–5) containing in their heterobicyclic structures the asymmetrical triazine template were performed with the use of differential scanning calorimetry (DSC) and simultaneous thermogravimetry/differential scanning calorimetry (TG/DTG/DSC) coupled online with Fourier transform infrared spectroscopy (FTIR) and quadrupole mass spectrometry (QMS) in inert and oxidizing conditions. All the compounds were thermally characterized in detail for the first time in this article. The DSC studies proved that the melting points of the tested compounds depended on the position and type of the substituent at the phenyl moiety, whereas they did not depend on the furnace atmosphere. All the tested polynitrogenated heterocycles proved to be molecules with high thermal stability in both atmospheres, and most of them (1, 3–5) were more stable in oxidizing conditions, which indicated the formation of a more thermally stable form of the compounds when interacting with oxygen. The simultaneous TG/FTIR/QMS analyses confirmed that their pyrolysis process occurred in one main stage resulting in the emission of volatiles such as NH3, HNCO, HCN, CO, CO2, H2O, NO2, aromatic amine derivatives, alkenes (for compounds 1–5), and HCl (for the compound 5). On the other hand, the oxidative decomposition process was more complicated and proceeded in two main stages leading to the emission of NH3, CO2, CO, HCN, HNCO, H2O, some aromatics (for compounds 1–5), HCl (for compounds 3–5) as well as the additional volatiles such as N2, NO2, NH2OH, and (CN)2. The type of the formed volatiles indicated that the decomposition process of the studied heterocycles under the influence of heating was initiated by the radical mechanism. Their decomposition was related to the symmetric cleavage of C–N and C–C bonds (inert conditions) and additional reaction of the volatiles and residues with oxygen (oxidizing conditions).