The warnlight at the dashboard is on and the computer says, that the thermostat works not right and the temperatur sensor don't work propper. How I can proof this and how if necessary i can repair or change this parts?

Most thermostats work the same. It's a simple and cheap system. The two wires will be for an engine sensor. It will most likely be for the water temperature gauge on the dashboard.

The coolant sensor temperature is usually found just beneath the cylinder head, on the engine block.

You just disconnect the 1-2 wires and then undo it with a wrench.
The sensor will look like one of these:
1999 Chevy Lumina ltz 3 8 v6 coolant temperature sensor Google Search

Just be aware .. you may have TWO such sensors on your vehicle.

One sensor (usually with 3-4 electrical pins) is near the thermostat and works in conjunction with other sensors to regulate fuel/air according to engine temperature.

The other type of sensor is in the block near the cylinder head. It sends a signal to the temperature gauge on your dashboard ONLY. If your temp gauge constantly reads too hot or too cold .. this one is the culprit.
If it's a running fault .. speed .. rough running .. fuel. It may look like this:

The best way to check a thermostat is to put it into a container of hot water with a thermometer and watch to see if it opens. The opening temperature is usually stamped on the thermostat somewhere. If you'd rather not remove the thermostat from the vehicle, you can run the engine for 5 minutes and see if the electric cooling fan cycles. Most V6 motors will reach operating temperature by then in springtime weather. Can't really do that if the fan is mechanical (attached to the motor). If Your temperature needle on the dashboard hasn't moved at all by 5 minutes, you either have a bad temperature sensor or the thermostat is stuck open. To rule out the temperature sensor, feel the upper radiator hose. If the hose is hot, your sensor is bad or has a bad connection. If the hose is cold, your thermostat is probably stuck open. If the thermostat is stuck closed, you'll usually have overheating and boil-overs from the coolant tank. Hope this helps.

Pop knows best,here's a guide to your coolant temperature.Here's the part.Easy to remove.

PO125---- Insufficient Coolant Temperature for Closed Loop Fuel Control

No idea what car or engine you have

If you have a coolant temp sensor it could be bad

The thermostat also cool be stuck open

Both could be bad

Without the correct coolant temp (thermostat) or temp
sensor working, then your running the fuel injector timing
off Computer Controlled Open Loop-- meaning the oxygen
sensors are not in use as in closed loop & your wasting
gas ,as you have only a preset control over fuel trim eg:
no adjustment as you drive

I would install new spark plugs if over 3 years old -nothing
else,tune-ups are long gone 30 years ago,only the plugs left,
don't go done that road of being pitched something you don't need

I would new install front oxygen sensors,not the rear ones,
if over 100,000 miles
New thermostat & coolant temp sensor (CTS) if that
is what you have or other correction for that situtation.

the antivirus has been playing whilst i have been at work so my codes programme doesnt work anyway firing up notepad and that has just locked up ,not my night tonight thats for sure .

P0124....Throttle/Pedal Position Sensor/Switch A Circuit Intermittent

P0128....Coolant Thermostat (Coolant Temperature Below Thermostat Regulating Temperature)

right got them from other computer and from what they say then you need to change the throttle sensor ,its on the end of the throttle pedal ,but the other one is easy to fix check that you have a thermostat fitted ,if you have then whats the local ambient temperature where you are as you may need to block off the radiator with a piece of cardboard to stop the wind chill factor

Coolant Temperature Sensor/Switch (For Computer): Service and Repair
ENGINE TEMPERATURE SENSOR
Removal




Engine temperature sensor, 5-cylinder
Jack up the car.
Remove protection cover from under engine.
Drain the coolant.
Lower the car.
Release coolant hose from thermostat housing using pliers.
Remove thermostat housing.
Remove sensor.




Engine temperature sensor, 6-cylinder
Jack up the car.
Remove protection cover from under engine.
Drain the coolant.
Lower the car.
Loosen oil reservoir for servo pump.
Remove coolant reservoir and put it to one side.
Remove screws and outer/upper timing-gear casing.
Remove screws and wire channel.
Disconnect connector.
Remove 4 screws and thermostat housing.
Remove sensor and wires.
Installation
Engine temperature sensor, 6-cylinder
Install thermostat housing sensor.
Position wires in slot on thermostat housing.
Note! The white marks should be positioned in lower opening of slot, from underneath.
Position gasket on thermostat housing correctly and install thermostat housing using two of the screws.
Position thermostat housing correctly and tighten the four screws.
Position wire channel correctly and position wire in channel.
Tighten screw on wire channel.
Connect the connector.
Install outer/upper timing-gear casing.
Install coolant reservoir.
Install oil reservoir for servo pump.
Follow-on work, 6-cylinder
Fill up coolant.
Warm the engine until the thermostat opens.
Switch engine oft and check the level. Re-fill if necessary.
Check for leaks.
Check in VADIS vehicle communication (read-out of parameter values), for current engine system, that the engine temperature shown appears
correct.
Engine temperature sensor, 5-cylinder
Install in reverse order.
Follow-on work, 5-cylinder
Fill up coolant.
Warm the engine until the thermostat opens.
Switch engine off and check the level. Re-fill if necessary.
Check for leaks.
Check in VADIS vehicle communication (read-out of parameter values), for current engine system, that the engine temperature shown appears
correct.

Thermostat and Coolant Temp Sensor is What I Recomend Replacing on this Vehicle

It may be temperature sensor on radiator. Dashboard gets info from it. If this sensor is not good, ac will stop and dashboard willl show some strange temperatures.

Had similar problem in my 2000 Jimmy. No hot air from heater. Had the shop (Midas) disconnect heater hoses at the fire wall and blow out the heater core with air hose. Got rust and junk blown out. Hooked up and flushed system with new anti freeze. Got lots of heat now.