Interpretation of retarding field analyser (RFA) measurements in flowing tokamak scrape-off layer plasmas requires a model of the perturbation introduced by the wake, or presheath, of the instrument. We extend a collisionless kinetic Mach probe theory to include a simple model of ion–ion collisions. Collisions lead to significant modifications in the downstream presheath. Depending on the ion-to-electron temperature ratio, flow speed and collisionality, the measurement obtained by averaging the apparent temperatures on each side of a bi-directional RFA is predicted to overestimate the unperturbed ion temperature, but with errors not exceeding 50% most of the time. The error increases with Mach number, and decreases with the ion-to-electron temperature ratio.