start the motor the temperature gauge goes to cold?

Yes, the cruise will not work if the engine is cold, I would swap out the engine coolant temperature sensor which should fix the problem. Here is the location of the sensor so you can swap it out. Check out the images (below). Let us know if you need anything else.

I finally got the temperature sensor replaced and it did not help the problem. The gage still drops to cold when the motor is started. i checked the voltage at the sensor when the motor was hot, and the gauge showed it was hot and got 2.6 volts. when i started the motor and the gage went to cold i still had 2.6 volts at the sensor. so, it looks like the sensor is not controlling the gauge. can't figure out what the problem could be.

When you say there are no codes did you do a CAN scan? You can get a CAN scanner (Controller Area Network) which will work on most cars from Amazon.

Here is a video to show you how:

https://youtu.be/u-4syLc-ifQ

and

https://www.2carpros.com/articles/can-scan-controller-area-network-easy

To me the gauge cluster or PCM will be bad, the temperature gauge is fed by the PCM, I would do the scan first to see if any cods are stored.