I have a 1jz, when the car is idled the temp will climb up to overheat, but when I start driving or when the motor is rev, the temp will SHOOT down to normal. I know it's not the temp gauge cause when I open the hood I could see a lil bit of coolant sprayed out of the radiator ( I don't have a overflow reservoir). So I'm thinking it's the water pump?

 

Yep, and/or the thermostat