If you can get your jug real warm, keep it inside like near the stove or something (mine is on a rack in the room here with the heater) then when you go out, keep it corked up inside an ice chest for insulation. It should stay warm in there. Get an old used plastic one, you can keep like spare chains and tools and whatnot in there as well. Just a small like six or twelve pack size cooler should work. Built in top handle for carrying, you know what I mean.
Another thought. if you could put your oil into a metal gallon can, you could slip it under the hood some place close to your warm truck engine while you are working. That should keep it warm enough to work good for hours. Floorboards on the way to the worksite with the heater blowing on it, then under the hood once saws filled up and parked. If you have to walk in a ways, put it into the plastic cooler.
hmm..you know, and they make cheap plastic one gallon Thermoses as well. Pour hot bar oil in there, it should stay hot then for hours.
That way you can have full strength good bar oil and not thin it with non bar oil stuff.