One problem related to radiator has been reported for the 2005 Toyota Matrix. The most recently reported issues are listed below.
Driver enters a small parking lot in san diego. Driver pulls up slowly to one of five perpendiculars stalls in the lot. As he is pressing brakes, the vehicle takes off, hits the concrete stop and then a frame wall a few feet after the stop. There is some damage to the bumper but none to the engine or radiator. Driver hits the steering wheel. Airbags do not go off. Wall is damaged. Driver puts the vehicle in reverse to pull back. The car takes off and lounges backwards, jumps the curb from the parking lot to the street, and starts moving backwards at high speed, smoking its front tires and doing a "donut" where the front wheels (this is a front wheel drive) are spinning and the vehicle is circling backwards. Finally at high speeds, the vehicle travels and slams backwards into a Toyota pickup truck stopped at the red light and stops. The backend damage is extensive and the rear left wheel is out of alignment. Vehicle is declared a total. This is a case of sudden unintended acceleration.