Method for determining, with geodesic precision, the position of a target point on a target object by using a geodesic measuring device, said method comprising a sighting device which comprises at least one objective unit that defines an optical line of sight, an electronic distance measuring unit, and a thermal imaging camera for recording a thermal image in the direction of the optical line of sight. An angle measuring function is provided for recording the line of sight alignment, and a control unit is provided for controlling the angle measuring function, the thermal imaging camera. In a thermal imaging mode when a measurement procedure is triggered, position data of the sighted target point which are determined in said measurement procedure are linked to temperature information which is read out from the thermal image for the target point at which the line of sight is aimed.