In this manuscript, we established coincidence point theory by using F-contractions within complete extended suprametric spaces. The results about coincidence points involve \((F_{\mathbb {C}_{P}})_{\tau }\) -proximal contractions together with rational \((F_{\mathbb {C}_{P}})_{R_{\tau }}\) -proximal contractions, with supporting examples included. The manuscript demonstrates the best proximity point theories and provides corresponding examples to reinforce the theoretical findings that operate under the developed contraction method. Moreover, we explore the fixed point outcome that culminated from these contractions, proving their applicability with real examples. The study investigates the relation between coincidence points and best proximity points as well as fixed points that arise from \((F_{\mathbb {C}_{P}})_{\tau }\) -proximal and rational \((F_{\mathbb {C}_{P}})_{R_{\tau }}\) -proximal contractions. Our theoretical findings gain practical meaning through an analysis of a nonlinear boundary value problem that stems from satellite web interactions. The differential equation that describes the spacecraft web structure thermal radiation behavior follows the Stefan-Boltzmann law. Through fixed point theory, we develop requirements that lead to finding unique solutions for temperature distribution problems. The analysis confirms how fixed point theory serves essential roles for addressing practical space technology problems with special relevance to spacecraft temperature research.
