I just bought a used 2008 A4 Avant quattro 2.0T. It has 50K miles and is very clean. Sadly, I've only had it two weeks and I'm already having a problem.

If I start the car completely cold, it runs perfectly, no matter how long or hard I drive it. If I stop it and start it right away hot, again no problem. BUT, if I start the car after a few minutes to a few hours of it last running, it starts up smooth at firsts, then after about a few seconds begins to misfire on #1. P0301 is the only code showing. It will then run rough and continue misfiring at any engine speed.

When this happens, sometimes I can run it this way for a while and wait for the car to warm back up, then turn it off and on again and the problem disappears. This isn't always successful, though. One time it resolved itself while running. Other tricks that seem to work are stopping/starting while moving, or revving the engine to 3000+ for a few seconds right after starting up.

Because it runs perfectly when started cold or hot, I wonder if this is a software or ECU issue? I can't work on it myself, but I'm looking for any other easy tests or suggestions for my mechanic.

Thanks!