That's an interesting idea. I looked and found that Honda's 1600 watt hand-held generator uses 1.1 gallons of gas in 4 hours at rated load. This would give you roughly twice the economy of running you vehicle engine (at .5 gallon per hour). And twice the heating time with the same amount of fuel. The question that remains is how warm can a oil filled space heater keep the passenger compartment of a vehicle? I may have to experiment with this. If it is capable of warming the interior well this could mean that your fuel usage could even be reduced further when the heater thermostat begins to cycle.
Also the only automatic transmission that I'm aware of that would have a problem with long term idling would be a Chrysler rear wheel drive hydraulic unit. Because the transmission cooler system is by-passed in park. But this can easily be rectified by placing it in neural.
Paul