Since it's an EFI engine, It shouldn't have a choke as there's no carbs. The ECM uses the data from the temp sensor to know to enrich the mixture when cold. I'd suspect the temp sensor has failed and is telling the ECM it's warm (even though it's not) and therefore no cold enrichment and runs well when warm. A scan tool will confirm my hunch, but most of us do not have one. A visit to a mechanic with a scan tool is probably warranted.
Please let us know what you find.

Chris