I believe it presently does. In fact, I believe that's the reason why the battery charge level dropped overnight in Musk's presentation of data and why, according to some folk, plugging it in to a normal power socket isn't enough to actually charge it as the battery pack draws more power than the socket can supply simply keeping the thing warm.

Such a process will of course drain the battery which still achieves the end result of 'can travel less distance on a full charge'.

I'm sitting in front of a 1500 watt radiant heater, it seems implausible that 1500 watts isn't enough power to keep a car sized battery pack in an enclosed space warmed to operating temperature.

For an idea what 1500 watts will do, I keep a 400 square foot room with only an R8 (US) ceiling and unheated space below at a 20°F differential to outside with this heater. It can't keep up when it gets too cold out, but my room has about 200 times the surface area of a Tesla battery pack.

Edit: maybe more than 20°F. I just shut it off for the day at °85F inside and 37°F out, so 48°F difference, but it is sunny, so the roof and two walls are warmer than 37°F. Data collection is hard. If only I worked in a uniform spherical room located in empty space…

I think the number I heard for heating the battery was 1.3kW. The model S battery is long and flat and hence has lots of exposed surface to lose heat. Also, it was in the teens when the original reporter left his car outside. So, is plausable.

Of course, for every hour of operation of the heater, you're using up about 1.5% of the battery capacity.

I'm rather thinking of being plugged in. 1500 watts is about all you can plan on drawing without blowing a breaker. The context, if I understood correctly, was that plugging in to a 120v household outlet was a net loss because 1500 watts was insufficient to warm the batteries to charging temperature and that presumably some numbskull in Tesla's software group decided to run the heaters even if it resulted in a net loss of power.

The explanation of the anecdotes is probably complicated, but I believe that the Tesla chargers monitor the voltage at the input to the car and reduce their current draw to keep a minimum voltage. So if your 120v transformer is a little on the low side (they vary) and maybe you used that 100' 16g extension cord you had handy, and maybe your house was wired when aluminum house wiring seemed like a good idea and that outlet has a bit more resistance between the wire and the terminal screw, you might be getting a lot less than 1500 watts. There could well be a point in the charging curves where there is a problem, but I don't think it is because 1500 watts isn't enough.

If you're plugged in, just charge the battery.

Would better thermal insulation help? Or it is already best economically viable?

I've no idea, I'm no expert in the tech. I'm sure 'better' would always help (though not necessarily overnight when it's a case of just slowing equalisation since you're talking long timeframes) but I don't know if there is a both better and economically viable process?