350z cold start

Does anyone have any data regarding my nightmare.

I have a 2004 Nissan 350Z Touring Roadster with manual transmission. It will not start the first time in the morning if the temp is below 30 degrees. I notice the thermamtor on the instrument panel will not change from tempicy to fuel economymph. If I change it then it will switch back to tempicy. Is there any information about this in your files. I spent $100 for diagnosis already and fear it will cost several hundred more. I cannot decide to spend or wait until spring. I am disabled though and need to keep my doctor appointments. Thank you for your help.