The present study investigates the impact of thermophoresis on soot capture in the clean cordierite porous wall of a diesel particulate filter (DPF). A three-step numerical model was developed, consisting of: (1) numerically reconstructing a representative volume of the cordierite porous wall, (2) computing gas flow through the porous wall using the lattice Boltzmann method, and (3) predicting of the DPF capture efficiency based on the time-dependent solution of a modified Langevin equation that takes thermophoresis into account. The validity of the approach was verified by carefully comparing the permeability predictions of a reconstructed cordierite porous wall to data from the literature. The impact of the magnitude and orientation of the thermophoretic force on the capture of soot particles of various sizes under different flow conditions was investigated. The thermophoretic force applied in or against the flow direction significantly affected the particle capture for the highest particle sizes and flow velocity investigated. Our results suggested that thermophoresis can potentially affect soot deposition uniformity in DPFs. Since the thermophoretic force mainly impacted soot capture efficiency in the presence of particle and flow inertia, a dimensionless criterion defined as the product of Stokes and Reynolds numbers is proposed to predict the onset of what can be called thermophoresis-enhanced inertial impaction. While similar results have been reported by others using simple flow geometries, this is the first time, to our knowledge, that this phenomenon is reported for a complex cordierite porous wall.