Interesting that you do not have the CEL so you would have no stored codes to assist in locating the problem. Those who have had the non functioning temp guages and the CEL the code has been the P0128 which is the tempeture has not reached the required temp in the required time. ie: it didn't get hot enough fast enough for the emissions system to function properly. And yours is only when it idles for longer periods so it may not be the thermostat in your case.

Please let us know what the dealer finds.

 

I've had a similar situation many time when I start up my HHR after it has been sitting in very cold temperatures. After the HHR has warmed from being driven for a while, shut down and restarted the temp gauge and DIC readout actually work.

I've never had a check engine light come on during this and have never had it checked by a service department.