I have an excellent question for physicists, and scientists; it regards lithium ion batteries.  Please read below for details. Can you help?

I'm guessing here

but here's my guess:

Guess #1 - the batteries are actually kept warm so that they are usable during very cold weather. This seems most likely given the heat generated by the "atomic battery".Guess #2 - the batteries simply aren't used during very cold weather

The problem with very cold weather is that it basically stops the chemical reactions going on in the batteries. It's not like they're going to explode or anything. Keep them above a certain temperature and they will function normally.

Given an "atomic battery" that functions by generating heat, it seems like it would be a simple thing to use some of that heat to keep the batteries in an active temperature range.

first of all , the batteries are packed in insulation to protect them from hot and cold . they are charged by solar panels , and are fairly  large compered to a mobile phone , that how . radio active material will supply the electrical needs and lithium , is fine for back up , just remember they will have solar cells to keep them charged .

The batteries are both heated and insulated.

There’s no “myth” about it. Just basic physics and chemistry. The batteries store energy and then release it through a reversible chemical reaction. ALL chemical reaction rates are controlled by temperature, chemical concentration, and agitation. 

In this instance there’s no agitation, the chemical concentrations were fixed when the batteries were first manufactured (and decrease over time) so the only real factor here is temperature. Frozen electrolytes cannot react much: so cold kills batteries. ALL batteries. But before that even occurs, colder electrolytes have slower molecules. Slower molecules interact with each other less often so the rate of chemical reaction slows down. 

How cold affects electronic circuits is totally different. Within limits, cooler electronics run better mostly because electrical resistance tends to rise with heat. But it’s totally different process.

You’re comparing apples with oranges.

This isnt an excellent question. They probably insulate and heat the battery via solar.

You have given the answer yourself : there is a long-lived power source on board.  It would not take very much power to keep the batteries at a reasonable working temperature.  I presume that there is other equipment which also requires a reasonable working temperature.  Why do you think that the Rover is permanently frost-bound.  You don't think NASA engineers haven't thought of that ?