I have a 2003 chevy impala. just changed the thermastat because the temperature was fluxuating. Since changing the thermastat the temperature gage constantly read in the red, however the coolant level has not changed and there are no visible leaks. What could cause this?

You probably need to bleed the cooling system properly.

Open the cooling system bleeder screws.

Slowly fill the cooling system with a 50/50 coolant mixture until coolant runs freely out of bleeder screws.
Close the cooling system bleeder screws
Install the coolant pressure cap
Start the engine.
Run the engine at 2,000 - 2,500 RPM until the engine reaches normal operating temperature. (midway on gauge)
Allow the engine to idle for 3 minutes.
Shut the engine off.
Allow the engine to completely cool.
Top off the coolant as necessary.
Run engine again at 2000 - 2500 RPM until the engine reaches normal operating temperature.
Allow engine to idle until cooling fans come on. It should come on with the gauge about 3/4 of the way to red. - if it gets to where is touches the red, shut down immediately.
When the fan comes on, put your hand behind the fan and observe the temperature of the air coming from the fan. It should feel hot. If it is blowing cold air, the coolant is not circulating through the radiator like it should. This could be caused by lots of things including an improper/defective thermostat, corroded water pump impeller, or a blown head gasket.

You have air trapped in system. There should be bleeder screws in thermostat housing and at the top of water pump housing. If that still doesn't work try using a vacuum system, may have to go to a garage for that tho

Did you bleed the air out of the radiator did you buy the correct temp thermostat didnt over fill the water in resevior you used antifreeze when filling back up did you flush the radiator temp sensor is it good are your cooling fans kicking on when there suppose to when engine temp reachs half way fans should kick on to cool radiator