I'm guessing that your soft case will not be a very good insulator compared to the styrofoam beer cooler I tested. To find out, put a small heater (5W 12V automotive lamp) inside the case, hook it up, and let it run for an hour. Use an accurate thermometer to measure the temp inside the case, and then the air immediately outside the case (ambient).
The temperature difference (in to out) will be the same you would achieve in the field with a colder ambient. If the difference is not as much as you would like on the coldest day, you need more watts in the heater.
On the coldest days, you can size the wattage of the heater such that you wouldn't need a thermostat. If the ambient is not as cold, then a thermostat would cycle on/off to reduce the average power in the heater.
I suspect that your case will have a substantial rate of heat loss, so you will likely need a 10 to 20W heater, which is within the capacity of a 12V 10Ah Sealed Lead Acid battery. 20W is 1.66A at 12V, so a 10Ah battery would keep your case warm for 6 hours.