What's so critical about the temperature being at 104 or 106F ? Does the volume of fluid change significantly with temperature?
How critical is the absolute level of the fluid, is there a +/- tolerance of fractional ounces by volume?
Is it possible to do a less-messy method:
Park in a somewhat level place to do the work, then open the drain plug and catch any that comes out and measure this into a separate container;
then remove the plastic overflow tube to drain out the rest and measure this into another container.
Now you know the volume held below the overflow tube (equal to the nominal level in an operating car), and the amount above that level when cold (equal to the active volume in the operating system that drains back to the pan).
Refill using an amount equal to the sum of these two volumes, this will put it back to the same level as it was.
This assumes there were no leaks and that the OEM fill at the factory was correct,
If you want to do a level check then start the car and shift thru the gears a few times to warm up the fluid, then open the drain plug and measure what comes out; this would be the amount overfilled. If none came out then add some until it dribbles out and put the plug back in. If you want to run a little higher level, then add a few ounces after the plug is back in so it doesn't dribble.
i can't believe that much precision is required when using a procedure to just add fluid until it dribbles out the overflow tube, but i'm happy to be proven wrong if all this is critical...
[edit] Well maybe i am wrong, according to OEM method that requires a vacuum pump, fluid pump and custom overflow tube as explained by Dr. Kelly