I didn't know there was a battery heater. So if there wasn't one, I'd be looking at a lot less than the 40 miles it's showing me on a 20º day? (And I know 20º can seem almost balmy to somebody who has to endure 0º or less.)
I'm just wondering if there's any validity to the claim that warming up the cabin before you start driving really has any effect on the miles you can expect on a cold day. I mean, they're saying that the cabin heat somehow penetrates into the battery compartment and warms it up despite whatever shielding the battery might have -- and that brief warming on a 20º day is enough to improve the miles. But then would the same work with really hot temps, and you should run the AC for a while before you drive when it's 95-110º? And would this only work on older Leafs that don't have battery cooling/heating?
The battery heater only protects from physical damage due to extreme cold. It kicks in when the battery itself (not the outdoors) has reached a temperature around -4F (-20C) to warm it up to around 14F (-10C) before shutting off. Provided that the Leaf is either plugged into power for charging, or if sitting alone, has at least 30% SOC or higher. This by itself won't give you more mileage, actually less in extreme cold since it is using power to stay warm (relative to the battery, not human related) if it is not plugged in to power, charging or not. The only models I'm aware of without the battery heater were the very first 2011 models. There has been discussions for years about creating a hack to activate the battery warmer earlier to aid in charging for example, but the heaters in the battery are designed to warm it up to avoid damage, not to be used as full time battery heaters to aid charging/driving in cold weather for example.
There is a valid reason to warm up the cabin in the Leaf when connected to power, mainly in range saving. The savings are the more useful when dealing with the Gen 1 Leaf (2011-2015) that uses the 24 kWh battery because they have the smallest "reserve" of power to work with. When you get into the Gen 2 models that use the 40 and 62 kWh battery, the range savings have a smaller effect, but still useful. It is true in the technical sense that warming the cabin up will migrate some of that heat down into the battery, but the effect would be so little as to be not useful. The cabin and battery pack are technically air gaped, so in extreme cold, the cabin heat won't make much of a difference.
Now, on the flip side, hot days, running the AC in the cabin will have little effect on a warm battery underneath as well. The Leaf is designed to be air cooled (by moving air) in the warmer climates. In cold climates, the Leaf is designed to heat the battery with waste heat produced either by charging or driving. If you live in a cold climate but you charge and drive your Leaf everyday, then the battery will stay warm and give you good charging speed and mileage. If you live in a cold climate and only drive or charge your Leaf with long breaks into between (days), then the battery has time to cool down to the outdoor temperature and if the outdoor temperature is below freezing, the battery follows that naturally.
Finally, why does warming up or cooling down the cabin (with power) save range? When the cabin is freezing, the Leaf uses maximum power to warm it up as fast as possible. This is why you can go from freezing to hot melting air coming out of the vents in less than a minute on most any EV. Once the cabin temperature has been stabilized to what you want, the amount of power to maintain the temperature drops a lot. On the Leaf for example, it can use 6,000 watts of power to warm up the cabin, but once the air temperature is stable, it might only take 500 watts, 750 watts, or 1000 watts to maintain the temperature, relative to the outside temperature. That initial load of energy is what saps range out of the Leaf, but when connected to power, it can slowly gain it back.
This works well on most L2 connections, but on a L1 connection (120V AC) connection that you are using, it can only contribute 1,440 watts of power at max. That just means the battery has to make up the rest of the missing power until the cabin temperature stabilizes and the power usage to keep that temperature drops below the max power your outlet can put out. The range saving effects of pre-warming the cabin are thus limited more when using a L1 connection (120V AC) versus using a L2 connection (240V AC) due to just plain ole' physics.