Doesn't say what if any tuning device is on the bike. Some of them allow controls (directly or indirectly) for cold idle. Might be something as simple as a problem you could straighten out by hooking up a laptop in your garage.
I wouldn't, however, just do a reflash of the ECM without knowing first if there's a tuning device that's been added and what kind. If it has been tuned a reflash of the ECM will likely either wipe out the tuning effort already done to the bike or potentially change the baseline under which that tune was done.
The OE basemap shouldn't have changed if that's all that's there. While it's possible that map was corrupted somehow it's probably not likely that would happen in a way that only effects cold idle. If it's been tuned at sometime it's very possible for that work to impact cold idle.
If the bike is running well, however, you don't want to change everything; which is what a reflash of the basemap might do. If the bike runs well after its warm and assuming it is a software related problem you're better served having someone correct the specific problem rather than tossing everything and starting over again. There are also a couple of sensors on the bike that could account for a cold idle problem. So might not be map related at all.
Certainly do need to get it sorted out. But might hold off on the complete reflash until a bit more is known about what's on the bike and more detail on the specifics of the potential causes.