The stability of a controlled network temperature control system (heat exchanger system) is examined in this study paper. A heat exchanger system keeps the end temperature of a liquid within defined parameters. The study proposes a linearized model of a temperature control system based on a delay-dependent state equation to accomplish this job. For a temperature management system in a network having time-varying delays, the LK functional (Lyapunov–Krasovskii) method is coupled with the reciprocal convex lemma. To get less conservative stability requirements, a new LK functional was assumed in the stability analysis, and the time-dependent of the (LK) functional was taken via the reciprocal convex combination approach. Finally, under the LMI (linear matrix inequalities) paradigm, the suggested stability analysis leads to a stability criterion. The suggested results establish a new stability criterion for a more accurate operating form for a present temperature control system based on a theoretically obtained temperature management system.