humming noise/splash shield

When the car is warm and I come to a stop, i hear a droning/whining type of noise. As i accelerate I hear it becoming louder and then it goes away ( I think) I've read about the failing fan pumps but I keep a close eye on the temp gauge and it does not move from the middle range.
I also need to get a new front engine splash shield as mine disintegrated on I-95 on Monday, was freaked out by the smoke coming from under the car but it was the plastic shreds hitting the exhaust. Does anyone else have the problem where the last 2 transmission shifts happen very quickly and the engine feels like its logging. I've been trying to figure out what is going on with my tranny and it shifts fine until 4/OD, which happen almost immediately.

What model year and engine (V-6 or V-8)?

-Rod

2001 Ls-v6 Automatic

Mine's made a similar noise since it was new. With 83,000 miles it hasn't changed. Mine is a 2001 v/8 with automatic and the noise isn't loud.