It is likely that the 3x priming is putting enough load through the battery to heat it.
Once it's been started the first time does it restart relatively easily? If so that's normal for Lithium.
14.4 volts when charging is perfect.
One other warning, if you charge a lithium battery below 0c you run the risk of coating the internal cells which reduces it's capacity and in a worst case could cause the battery to catch fire. If the conditioner doesn't switch off at low ambient temp I'd suggest unplugging it until the weather warms up.
Before I found out about Lithium batterie's low temperature "quirk" if it was cold I used to have to turn the engine over for 30 - 50 seconds before it would fire up. Once started it was fine for the rest of the day.
