It must be vapor locking. The motor is a mid engine design and there is a cooling fan like one on the FJ60 that is not running when the motor is on or off.
I guess it should turn on when the motor is turned off.
The guy said that the last owner had a problem that the motor would shut down when it got hot but this owner never had that problem but he got it in Oct. 07.
I am not sure if the rear motor fan should run when the motor is on but if it should I bet that would be the problem.