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TO get back to your original question: How long will it last? If we assume that the battery rating is accurate, 18V * 9 A-Hours=162 Watt-hours. Lets say the AC conversion is 90% efficient, 162*.9=146 W-hours146watt-hours/125 watts=1.17 hoursYou would do a little better with a DC heater, but not much. I assume all you need to do is warm it up enough to get it started, but I think you might do better to get this thing a tune up, and use some multi-vis oil to handle the cold. If that does not work, my grandpa used to slide a flake of burning straw under his model t to warm up the engine on cold Wisconsin mornings, but your Honda might have too much plastic to allow that.
You might see how warm you can get it on 1 battery. I realize it is not ideal, but you might get away with running a battery worth of power into the heater, then trying it. Kind of the modern equivalent to my grandpas straw, but safer. You don't need to get it all the way to 100 degrees, just above freezing, I am guessing.If I were going to try a setup for this, I would assume you have 3 issues at very cold temps: 1. The battery for your starting does not have as much current capacity when cold. We used to turn on the headlights for this in a car, then try to start. You could put the battery on a heating pad, or, if you used the starting battery to heat the engine a little, the load would heat the battery. I am assuming you have a smaller sealed battery to heat the Honda. If you borrowed the deep cycle battery from your boat for the winter, I bet you could spin the motor much faster, regardless of how thick the oil is.2. The oil is cold, which slows cranking. You could put an inverter off the deep cycle battery, and run a heater like you originally planned. A deep cycle battery should have over 100 AH at 12V, which should be 1200 WH, much more than a tool battery. If you want lithium for the longer life, I just got a 105 AH LION lithium battery at Costco, but it was over $7003. The fuel does not want to vaporize. Here the old solution was a can of ether, now we use fuel injection. There are just starting to be fuel injected generators- have not seen 7 KW yet. That is probably the solution you want longer term- I assume thatchy will also be more efficient, and a 7KW probably uses enough fuel that this would matter. The only other possibility is a propane system. I assume you don't have gas plumbed in, since you are on generator, but they can be converted to run on propane. These systems are designed to start when the power goes out, and I would bet they are tested to work when it is very cold.:
Thank you for all the comments, will probably just end up using the Milwaukee unit for powering lights in the shacks.
Do a review of the Top Off ..thinking about getting one for at home use ..got enough 12 v options for my on ice applications.