A molecular descriptor, also known as a topological graph index, is a mathematical formula that may be implemented to any network that reflects a molecule structure. This index can be used to explore some physical aspects of a molecule and examine mathematical values. As a consequence, it is a better solution for costly and time-consuming laboratory experiments. In this work, we calculate the first temperature index, the second temperature index, the first hyper temperature index, the second hyper temperature index, the sum temperature index, the product temperature index, the reciprocal product temperature index and the $F$-temperature index. These defined indices are computed for the Non-KuKulean benzenoid graph.