It is almost certainly NOT the cold start valve. If CSV fails, car will be miserable hard to start at all. If car starts fine, just won't idle, it is NOT the CSV.
There is an idle air valve on the FI cars that needs to be open when cold. Is easy to check, just look inside cold and hole should not be blocked.
There are some wonderful troubleshooting info on the web somewhere for these. Check, test before replacing expesive parts.