Easiest/most affordable way to boost voltage?
Before you do anything.. make sure the rest of the circuitry operates within spec at -40C. If it doesn't, getting more life out of the battery is moot.

Further, you need to work out what the power output of that battery is at -40C. If it is less than your required power level plus conversion efficiency, you will not be able to boost it. 

If, and only if, those are within tolerances, there are numerous buck-boost regulators available online you can use. Some will be termed as "Joule thief" circuits.

Your other alternative is to make the device self-heating. That of course involves sacrificing some controlled battery current to keep the device warm enough and some clever thermal insulation to keep the cold parts warm using minimal current while still allowing you to cool the hot parts.