I've thought about that before, but I don't see it working well. You'd definitely want to be running the inverter off of a 2nd (or 3rd or 4th) battery. Probably have to store it in the back, run wires, etc. More cost/hassle than it's worth.
While I plug my block heater in at home, I can't at work. Would be nice to have it on a battery/timer so my car heats up fast on the way home, too. Or maybe I just need to find someplace to plug in at work.
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View my fuel log 2015 Mirage ES 1.2 manual: 44.1 mpg (US) ... 18.7 km/L ... 5.3 L/100 km ... 52.9 mpg (Imp)