Sorry, I've put you wrong there. You shouldn't use a comparator with a reference voltage for detecting the temperature. You need the voltages at both comparator inputs to be proportional to the battery voltage, because the battery voltage will vary as it discharges.
So you need a two-resistor voltage divider at one input, and at the other input, a voltage divider made from a resistor and your thermistor.
I thought you might also want to monitor the battery voltage, so your "always ON" LED turns OFF when the battery voltage is low. In that case you do need a reference voltage, and a MAX9043 (http://www.digikey.com/product-detail/en/MAX9043AEUB+/MAX9043AEUB+-ND/1495090
) looks like a good option - it has two comparators and a separate reference voltage.
You'll want to minimise load current on the battery, so use high resistances (in the hundreds of kilohms) in all of your voltage dividers. Assuming you can't use a different thermistor that has a higher resistance, you can still minimise the current consumption in that leg of the circuit by using a high resistance in series with it, so you have a low voltage (e.g. 0.1V or so) across the thermistor. You will have to use a similar resistance ratio in the leg that feeds the other comparator.