Hard starting when engine is hot?

Checking the fuel pressure from the aux pump is literally the second thing I do on preflight, after turning on the master power.  Noting the voltage drop on the battery while the pump is running gives me an idea of battery health at the same time.

"..The only evidence I have that my aux electric pump is functioning properly is that is sounds right and that if I turn it on before hitting the starter button the engine starts more easily..."

I´m not an expert but in my opinion this should not occur because the main pump should be enough to handle the start and the overall engine needs regarding fuel.

There are only 2 situations that the aux. pump makes a difference:

1. First start of the day engine cold and the fuel lines not pressurized. In this case 10 to 20 seconds of aux, pump is sufficient to prime the line then you can turn it of and the start will be fast only on the main pump.
2. When engine hot with the plane sit for long time it is god practice to do the same to remove from the fuel line any vapors and put fresh fuel on it. After that you should be able to start your engine without the aux. pump, no difference should be noted with the aux. on or off after the priming of the line.   

Genival,

Your "1" and "2" are in fact the situations in which I can say that having the AUX pump on for starting does make a difference.

Yes AC

The only difference is that after priming or pressurizing the fuel line you should start the engine without any even with the aux. pump turned off.

Remember that the aux. pump is a backup that is why you should turn it on on takeoffs and landings because if any issue occurs with the main pump it will avoid and engine stoppage in a critical part of the fly