The car will run rich when first started especially on very cold mornings. This is done on purpose to allow the engine to start and run properly, once the engine is hot their is no need for a rich mixture and less fuel is added. It works like a choke when you used to have to pull them out then push them in when the engine was hot, but now the ECU
takes care of all that for us
Also just below half way on the temp gauge is fine, near the bottom/in the blue I would say a faulty sensor, at the top/in the red then could be a faulty sensor or overheating but from what you say I think your fine.