Hi and thanks for using 2CarPros. Com. It sounds like you have everything working the way it should. My only concern is if the thermostat was installed correctly. Here are specific directions for your vehicle. Scan through them to ensure directions were followed. If they were and you still have the issue, chances are you have a sticky new thermostat. These directions also include how to check the part.
2000 Lexus GS 300 L6-3.0L (2JZ-GE)
Vehicle  Engine, Cooling and Exhaust  Cooling System  Thermostat  Service and Repair
SERVICE AND REPAIR
REMOVAL
HINT:
Removal of the thermostat would have an adverse effect, causing a lowering of cooling efficiency. Do not remove the thermostat, even if the engine tends to overheat.
DRAIN ENGINE COOLANT
DISCONNECT WATER INLET FROM WATER PUMP, AND REMOVE THERMOSTAT
a) Remove the 2 nuts holding the water inlet to the water pump, and disconnect the water inlet from the water pump.
B) Remove the thermostat.
C) Remove the gasket from the thermostat.
INSPECTION
INSPECT THERMOSTAT
HINT: The thermostat is numbered with the valve opening temperature.
A) Immerse the thermostat in water and gradually heat the water.
B) Check the valve opening temperature.
Valve opening temperature: 80 - 84°C (176 - 183°F)
If the valve lift is not as specified, replace the thermostat.
C) Check the valve lift.
Valve lift: 8.5 mm (0.335 inch) or more at 95°C (203°F)
If the valve lift is not as specified, replace the thermostat.
D) Check that the valve is fully closed when the thermostat is at low temperatures (below 40°C (104°F) ).
If not closed, replace the thermostat.
INSTALLATION
PLACE THERMOSTAT IN WATER INLET
a) Install a new gasket to the thermostat.
B) Align the jiggle valve of the thermostat with the protrusion of the water inlet.
INSTALL WATER INLET Install the water inlet with the 2 nuts.
Torque: 9.0 Nm (90 kgf-cm, 80 inch lbs.)
FILL WITH ENGINE COOLANT
START ENGINE AND CHECK FOR COOLANT LEAKS
Let me know if this helps or if you have other questions.
Take care,
Joe
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Tuesday, May 29th, 2018 AT 8:31 PM