the thermostat costs only about $10. you need to drain the coolant though.
many factors may be involved in your car problem, therefore, thermostate could be only one of them. if not caused by thermostate failure, you need to check them one by one,for example, the injector (check the resistance), the ignition coil(check the resistance), to find out which cylinder doesn't work well.
in fact, you didn't tell us the engine shaking when it is in idle, or during speed up. if the car shakes during speed up, it is another story.