Take the battery indoors with you. Keep in mind that a freezing cold battery has less than half the cranking power. A full tank of #1, plus a warm battery may make all the difference you’ll need.
While taking the battery inside might very well allow starting the next morning,something to consider is how practical this will be. Depending on the vehicle,it may well have dual batteries,neither of which will be particularly easy to remove/replace at -40F. I’ve done this before under those conditions w/satisfactory results,but it was a gas car w/ single battery.
“Take the battery indoors with you.”
That sounds like a better idea than keeping the car running all night.
GSC - are you sure there is no indoor parking available?