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The "low" oil temp reading is normal if the oil temp is below about 15*f. I've seen it before. The odd (but also normal) thing is, it will retain that low reading on the DIC even as the car warms up to normal operating temp. If you shut the car off once warmed up, and restart, then you'll get a correct actual reading. That is apparently just a quirk in the software that few people ever see, since most don't drive their Vettes in single digit temps.
I highly doubt you are seeing that cold of temps in La, so I'd be willing to bet it's a sensor issue.