This study proposes a modified collocated parameter model to estimate the effective thermal conductivity (keff) of two-phase wire mesh materials. The study focused on the influence of parameters, primary as well as secondary, on the effective thermal conductivity of a wire mesh, namely, thermal conductivity ratio (α), concentration (γa), mesh number (M), and thermal contact conductance at the wire-to-wire interfacial area were all investigated in detail over a different temperature range in the normal to the wire mesh. The analytical expressions for effective thermal conductivity in the form of algebraic equations were derived by adopting the solid square cylinder unit-cell-based thermal resistance method for a three-dimensional spatially in-line touching periodic medium. The effective thermal conductivities of different wire mesh materials with solid–fluid combinations, possessing conductivity ratios of 1–10,000 and concentrations of 0–0.8, are predicted for various temperatures at constant pressure regimes using the developed model. Furthermore, the developed model was applied to estimate the effective thermal conductivities of brass and stainless-steel wire mesh, which are compared with values measured using the modified transient plane source (MTPS) instrument over the temperature range 283–460 K. For the brass and stainless-steel mesh—water, silicone oil, and air combinations, the estimated values of effective thermal conductivity obtained from the present model show an average deviation of fluids ± 2.6%, with air ± 4.4% in the z-direction, respectively, concerning the ones obtained from the experiments.