Not sure what you mean by "going through all the gears", as a CVT has none.
But, I would go to get it serviced and ask about a "teach-in" procedure to be performed on it. If there's anything wrong with the functions of the transmission, that procedure will definitely bring those to light.
Generally speaking, any turbocharged or automatic transmission vehicle should NEVER be driven cold. Most transmissions require operating temperatures of anywhere from 70-80*C (yes, Celsius, not Fahrenheit for US drivers) before safely driving. Of course, most drivers (including my wife) don't really care. Especially with a 10-year warranty. Then again, it's always up to the gearhead husband to worry about what's broken when it does start sounding or feeling off.
I maintain further that with these newer cars with aluminum blocks, pre-heating an engine should always be done before driving.
Red Cross --- Might seem elementary, but try starting the engine tomorrow before taking your morning coffee. And don't start your drive until the temp gauge shows at 40 to 50%. That will mean that the engine oil is actually at optimal driving temp. See how that works. Regardless of the temperature outside.
Then, if you're looking for more reasons to spend money --- if your Cross in your region doesn't come with installed transmission oil heaters, then see about doing that - but check with your dealer to ensure that doing so will NOT void your warranty.
If all else fails, you may have to get a brand new Jatco transmission! Wheeeeeee!
... F*cking Jatco.