The effect of temperature on the liquid-gas interface and consequently on the capillary pressure in unsaturated dead-end pores is conceptually modeled in this paper. Trapping of non-wetting fluid (e.g., air) in the dead-end pores impacts the capillary pressure-saturation relationship and affects the continuous flow of wetting fluids. In the dead-end pore, which is assumed to be a simple vertical cylindrical capillary tube with one end closed and the other end open to the liquid body, the dependence of solid-liquid and solid-air interfacial tensions on temperature and its subsequent effects on the contact angles are deduced. A non-linear ordinary differential equation, using the Young-Laplace equation, in terms of a contact-angle-sensitive temperature function is derived and numerically solved using the fourth order Runge-Kutta method. This temperature function is used to obtain the capillary pressure-temperature relationship for a solid-liquid-air capillary system. Two example problems, first a glass-water-air capillary system and second a polytetrafluoroethylene-n-hexadecane-air capillary system, are solved here. A linear decrease in capillary pressure with temperature is observed, suggesting that entrapped air affects capillary pressure in dead-end pores. A similar linear decrease in capillary pressure, consistent with experimental observations, is observed for open-end pores.