On the consistency matter . . .
IF you're pumping to as nearly the same level in the tank as you can, and IF we can assume that the temperature of the fuel being pumped doesn't vary by much (by virtue of being insulated underground from variations caused by weather) both the overhead and hand calculations should produce relatively consistent calculations (not to each other, but each relative to itself -- I'll come back to that at the end) , regardless of any temperature change in the fuel after pumping. The overhead, though, has more potential for variance.
Assume all underground fuel is at 60*. Pump 30 gallons that happen to weigh 225# at that temp. Then park the rig and go back to the trailer and sleep. While you're snoozing, old man winter cools the fuel that is now in your tank to 30*. Assume the 3% loss of volume that someone mentioned earlier is the correct factor for getting the density of your now cold fuel. You now have about 29 gallons, but it still weighs 225#. (My physics professor would kill me -- the correct way of stating it is to say that the fuel still has the same mass -- 102. 04 kilograms) All of the diesel molecules are still there, they're just closer together.
Then several things can happen. First, let's look at the overhead. Say your fuel heater at the filter increases the fuel temp back to 60*, just where you pumped it. If the overhead is truly and accurately measuring the VOLUME of fuel delivered, it will accurately calculate miles per GALLON based on volume of fuel pumped. If you have no fuel heater, you will pump the cold fuel to your injectors, but you will be lighter on the go pedal, because it takes less VOLUME of fuel (therefore, less pedal) to supply the same number of diesel molecules to the injectors, but the overhead will see less volume and show higher mpg. Conversely, if your fuel heated up to an ambient 85* in the truck's tank while you're sleeping, you'd have to go heavier on the pedal to get the same mass of fuel into the engine, but, since we don't have fuel chillers on or trucks, you haven't cooled the fuel back down to 60* and the overhead will have sensed more fuel flow and will show lower mpg. All of this assumes a constant temp for the air supplied for combustion, which we know doesn't happen.
Now the manual method. Remembering the assumptions that you are filling to a consistent level with fuel of a generally consistent temperature, you will, from tank to tank, be basing your calculations on fuel of a similar density and an odometer that reads consistently (discounting the miniscule tire tread wear between fill-ups). It will generally be a more accurate indicator of your efficiency because it is based on mass of the fuel rather than volume. Consistent fuel temp at the pump means consistent density of that fuel, so you will be calculating on an average that eliminates any variation of the volume of the fuel.
For all of that I agree with (I can't remember who

) up above, and pay little mind to minor variations from tank to tank. Given the potential for variability in my assumed constants (fill level and temp of pumped fuel), there are too many other variables. Above 50 mph or so, wind resistance becomes a bigger factor than rolling resistance, thus quartering in and out of a 15 mph head or tail wind as the road winds will have an effect that would require more than I can measure and more intricate calculations that I can (or am willing to) do. How much did I use the Jake? Did I hit the stop lights or not? When didi I last check the tire inflation? And on and on . . .
I calc by hand (in my head, actually), and would only be concerned by a significant variation in mpg from my last calc under a similar load.
It would be more accurate if we could figure efficiency on miles per pound (or, more accurately, kilogram) of fuel, but that ain't gonna happen.
Sorry for being so long-winded.
Perfesser Haggis