Ok, I got it home today and started checking things out immediately. When I was backing it off the tow truck bed and pulling it into my garage I noticed that I could floor the gas pedal and it didn't really respond at all. It just kind of idled into the garage.
Once I got it into the garage I popped the hood and peeked under the engine cover to see what I could see. I immediately noticed a connector that wasn't connected to anything. I looked around for where the connector went and found it right away. I recognized it as the fuel temp sensor from my earlier research. I plugged it in and got back in the car and started it up. It was a little hard to start, but it started after about 3 seconds of cranking. I put it in reverse and tried to back out of my garage. Again I could floor the pedal and wouldn't get a response. That changed after about 30 seconds of coaxing it out of the garage. It started to pick up and run pretty good. I drove it around the block about 5 times without stalling. Then I decided to drive it to the gas station to get some diesel (it was on 1/8 of a tank). I put 4 gallons in and got back in the car and drove it back to my house with no stalling or anything. I thought things were good.
Back in my garage I got out my OBD-II code reader to see if I was still getting codes. No codes, so I cleared the CEL. I started it again and drive it around the block one more time and then back into my garage to park it and go into the house.
I called my dad and told him I was going to bring it down to his house (about 3 miles from my house) to show him the car. I get back into the car and start it up (it's still a little bit hard to start), put it in reverse and start to pull out of my garage when it stalls. I started it again, put it in reverse, gave it gas, and it stalled. this happened 3 times. On the fourth try, I decided to make sure it was getting good gas before putting it in gear by revving the engine up a bit. This time it worked and I took off to my dads. It drove fine all the way to his house, even through several stop signs.
I picked my dad up and we drove it around a bit without issue, I then drove it back to his house and shut it off. It was off for about 10 minutes when I started it back up again and tried to back out of his driveway. It stalled again. I was able to get it going the same way I did before and drove it all the way home.
When I got it home, I turned it off and back on a few times to study how it was running. It's a little bit hard to start every time I leave it off for more than 5 seconds, and it idles slightly erratically between 900 and 1000 RPM in park. The CEL never came back on.
There is no evidence that the TB has ever been changed and it has 158K on it, so I am going to schedule that with my mechanic tomorrow. He did my 03 TDI GL for $800 including parts and labor and did a great job.
So, what do you guys think now that you know more about it's behavior?