We examine the effect of an indoor-outdoor temperature difference on the transient wind-driven cross-ventilation of a room. Laboratory experiments are performed in a water flume using a reduced-scale model room. For solely wind-driven cross-ventilation with no initial temperature difference between the room and the external fluid, the ventilation rate is constant. In experiments, the mean dye concentration decays exponentially, which is expected when the room remains well-mixed. When there is an initial temperature difference but no wind, the buoyancy-driven exchange-ventilation results lie between a model that assumes the room is well-mixed and a new model that assumes no mixing between the incoming flow and the room. When both wind and buoyancy drive the flow, the relative importance of these two effects can be described by a Froude number, Fr. For buoyancy-dominated ventilation (Fr<1), the ventilation rate through the windows can be modelled using an exchange flow with a Fr correction to account for wind effects, which can increase the ventilation rate by up to 40%. For wind-dominated ventilation (Fr>1), a temperature difference slightly reduces the ventilation rate, but only by up to 6%, a change that can be neglected in most applications. Two processes compete to ventilate the room in combined cases: the removal of fluid from a lower layer by flow through the windows and the erosion of an upper layer by entrainment into the jet that crosses the room. The relative rates of these two processes depend on the geometry of the room.