X5 stalling hot

My 2001 X5 3.0 has this problem of stalling after idling a long time. If you sit in park with the engine running for maybe 20 minutes, then drive away, it stalls out after about half a mile. You turn the key off and it starts right back up again but the first time you start it, some of the dash warning lights stay on. They go out if you pull over and stut it off, then start again. This only does this when the vehicle is hot, and left idling for a prolonged period. I pull over to take cell phone calls and will sit for long periods with the engine running, sometimes with the AC on. Put it in drive and within half a mile you can feel the engine shutter, and then die. It definitely feels like lack of fuel. Any ideas?

Have you had it tuned in the last 100K miles?