It all depends on whether the plug is tapered or has parallel sides. To the best of my knowledge, most
modern cars have drain plugs with straight threads, not tapered, and rely on a washer/gasket to ensure the seal.
In the days when I used to service my own cars (circa 1970's and '80's), the drain plugs tended to be tapered. They also had 'female' square heads, into which one fitted a 'male' square wrench - a lot like a grub screw and allen key arrangement, but square. Some cars had straight plugs with gaskets for the sump and tapered plugs with square holes for the gearbox and differential.
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The plug on Kando's tractor appears to be tapered.
I have never taken my car to a quick-lube place, so I can't comment on how they do things. Might they vacuum the oil out?
Another option, other than letting the engine cool, is to insert the tapered plug
just tight enough to allow it to be in contact with the sump to allow heat to transfer from the sump to the plug. Once the plug has reached the same temperature as the sump, torque the plug to specs.
Do most tractor owners tend to drain their oils while the engine is hot or cold?