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A self-consistent steady-state 2-D kinetic plasma solver has been applied to the problem of Langmuir triple-probe plasma diagnostic measurements in a flowing collisionless plasma. The triple-probe response is simulated for ion Mach numbers M = 0 - 5 and probe radii rp = 1 - 90 lambdaD (Debye length). Results indicate that a high probe radius and high ion Mach numbers more closely approximate the ideal thin-sheath triple-probe response. Small probe radii on the order of the Debye length can result in temperature errors of the ideal model greater than 70% for a probe bias of 20 V. An analytical approximation is described, approximating triple-probe measurement offsets given arbitrary probe bias and probe radius and ion Mach numbers 0 < M < 5. The fitting error from this analytical approximation is estimated at 2%-6%.