Yes the oil will thin and run faster as it warms. In a shop with no heat at night the oil will be cold in the morning and thicker, it will thin as the shop warms and thus the oils warms also.
But, in a house or shop at mostly a constant 70F air temp, using oil at room temps also near 70F, and not placed right at the burner where it will heat execessively, then the flow should be more constant and the oil should not be thinning out since it should not be changing tempature much. Still watch it anyway, don't want any accidents, but constant adjusting should not be needed in normall continueos use.
Something I am experimenting with the last couple days, soaking a piece of wood in the oil then tossing in the fire. For people just wanting to use up what little kitchen waste they have this might be worthwhile also. I decided to try this when the wife cleaned the deep frier and I now have about 5 quarts good clean oil to play with. She said the french fries taisted funny last time she cooked them. I think the oil was fine, it was the potatoes were different, oh well!
If you can do it without making a big mess, I think soaking some smaller wood pieces in oil then tossing into a hot fire onto the hot coals worked well. Kinda a candle/wax/wick type effect. Maybe soak the wood in oil in a large coffee can, then place in an empty coffee can to drip dry. When you want the extra heat toss a few oily pieces into the fire. Only did a few, so far it worked nicely for me.
If you try it, BE SAFE and use some sense, don't load the whole wood burner all at once with oily wood! Only use a small amount and watch and learn how it's working for you before using larger amounts!!
I also dumped oil from a soda can alot at a time onto wood not yet burning in the fire and directly onto hot coals. Onto hot coals was a good hot fire quickly, the oil on the wood burned well too, oil that ran off the wood and into the coils burned well. Seemed to be a clean fire. Not all sooty nor oily smokey.
I poured in alot of oil at once to see what happens. It burns of course
But the ashes is what I wanted to know about! The cool oil in the ashes was not that bad. I should pont out I don't use a grate, I just sit my wood in the bottom of the burner. So when I needed to add more wood I just stired the ashes around a bit and the hot coils burned the oil in the ash. I now seem to have clean ashes (not oily) and I had dumped alot of extra oil.
2 things to point out though. First I have been getting a kinda sweet funky smell, not sure if that is because of a new pipe I installed and high heat, sometimes they do that alittle at first, or if it was from the oil I was burning. Only noticed it with a really hot fire. Could be due to using too much oil at once?
And I do not recomend dumping in lots of oil at once. I have not yet checked my pipes. If the oil gets hot fast and not enough oxygen to burn it fully it could basically steam into the pipe and condense there causeing problems!!!
I didn't do enough to be able to check for that, if it happened I'll know it did, but if it hasn't yet then I won't know if it will! I was just trying to see how much of a mess I could make, and I had no mess left over to worry about cleaning out. I just stirred the ash and the oil burned out of it.
I geuss if like most people you are using a grate to hold the wood, then any unburned oil dripping into the ashes could make a mess to clean. If not using a grate, just stirring the ashes once in a while with the hot coals seemed to work fine.
Using a proper slow drip onto hot coal and burning wood is the best and should have no problems.