This article presents the results of computations on pilot-based turbulent methane/air co-flow diffusion flames under the influence of the preheated oxidizer temperature ranging from 293 to 723 K at two operating pressures of 1 and 3 atm. The focus is on investigating the soot formation and flame structure under the influence of both the preheated air and combustor pressure. The computations were conducted in a 2D axisymmetric computational domain by solving the Favre averaged governing equation using the finite volume-based CFD code Ansys Fluent 19.2. A steady laminar flamelet model in combination with GRI Mech 3.0 was considered for combustion modeling. A semi-empirical acetylene-based soot model proposed by Brookes and Moss was adopted to predict soot. A careful validation was initially carried out with the measurements by Brookes and Moss at 1 and 3 atm with the temperature of both fuel and air at 290 K before carrying out further simulation using preheated air. The results by the present computation demonstrated that the flame peak temperature increased with air temperature for both 1 and 3 atm, while it reduced with pressure elevation. The OH mole fraction, signifying reaction rate, increased with a rise in the oxidizer temperature at the two operating pressures of 1 and 3 atm. However, a reduced value of OH mole fraction was observed at 3 atm when compared with 1 atm. The soot volume fraction increased with air temperature as well as pressure. The reaction rate by soot surface growth, soot mass-nucleation, and soot-oxidation rate increased with an increase in both air temperature and pressure. Finally, the fuel consumption rate showed a decreasing trend with air temperature and an increasing trend with pressure elevation.