Fuel gauge reading high

[Mitchell Segal]

Hello all,
I have a 2001 Audi A4 1.8T Quattro, and I've noticed a bit of a problem with my fuel gauge recently.  It's always been a little generous on the reading of the top 1/2 of the tank (Used to get about 400km on the top half, and then about 325km on the bottom half).  
But lately, it's been getting even worse.  On a recent tank, I got to about 500km before the gauge read 1/2 way, but only got another 220km before I was in the red.  And even once I hit the red, I used to get about 60-80km before I would run out of gas, but recently, about 5-10km after the low fuel warning symbol came on, the car started acting funny, like it was running out of gas, so I quickly pulled in and filled up, and then everything was fine again.  Now I get nervous and fill up before I even hit the red zone.
Another thing I have noticed as part of this change, is now after you start the car, for the first 10 min or so, the gauge actually creeps up about 1/8 of a tank in the reading.  So I'm thinking that the true reading is what it shows when you first start the car, but that after driving it a few minutes, it's actually reading about 1/8 tank higher than it really is.  I also notice this in the trip computer, when you look at your distance to empty reading, when you first start the car it might say 200km to empty, but after 10 minutes of driving, as the gauge moves up, the distance to empty will actually climb along with it, and suddenly it's telling me I have almost 300km to empty.
It's almost like as some component "warms up" with use, it's causing a higher than normal reading on the gauge.  Anyone have any ideas?
Is it the gauge, or is it the level sender in the tank itself?  Anyone else experience this type of problem, and fix it?  How, and and how much did it cost?
I can live with it, but if it's an easy fix I can do myself, and the parts aren't too expensive, then I would like to take care of it.  Right now, I'm basing my fillups on the trip meter, and having to subtract 1/8 tank from the gauge reading, as I don't want to risk running out of gas.
Thanks
Mitchell