Cancer is a life-threatening illness. For the treatment of various forms of cancer, there is currently no medicine. To combat this condition, new medication studies are being carried out. HDAC-based multitarget medicines are one of them. The characteristics of the molecular graph can be expressed numerically using topological indices. Topological indices can be utilized to offer details on the physicochemical characteristics and biological properties of molecules in investigations of the structure-property relationship (QSPR) and structure-activity relationship. Theoretical and statistical research on drug-like molecules helps drug design and discovery by rationalising lead identification, immediate judgment, and mechanisms of action comprehension. In this paper, we calculate temperature-based topological indices using the analytically closed formulae of various molecular structures of anti-cancer medications such as vorinostat, tucidinostat, triciferol, CUDC-101, and CUDC-907.