Odd/Irritating Start Problem

I haven't read any codes yet, but here goes:
2000 Winstar SE -- when the engine is cold it starts fine, idles fine (now that I've replaced the IAC). Engine runs fine all the way to full operating temp (i.e., when cooling fan comes on). Shut off the engine, say long enough to run into the store 10-30 minutes, and it won't restart (stay running). RPM's come up then it immediately dies. Hold gas pedal down and it will start but idles roughly for a while. Let engine cool down for an hour or so - long enough for temp gage to read 1/4" above C and it will start as if engine is cold. Putting in a new MAF tonight but I don't hold much hope that's it (tried cleaning it but that had no effect). So I conclude it is coolant temp related. I have an OBDII on order so I should be able to get the codes.
BTW, except for the U-Haul trailer harness I begrudgenly/mistakenly had installed (and have since ripped out - killed a battery) I really like the van. Rides nice, handles nice. Better half loves it!

Could be temp sensors or crank position sensor. See what codes read and post back.

I certainly will post the codes as soon as I get them. Update: I installed the new MAF last night (5 minute job when you have the correct security bit) and drove the van to the conditions in the original post. Remind me to add dielectric grease to the round, external MAF connector. It had none - never did. Seems it should. Also, better half drove it today, and van seems to perform as well as it ever has. No more hot start problems, and a nice smooth idle. As a matter of fact, we rely on the tach (and lack of panel lights) to tell us whether the van is even running! I would not have expectd the MAF to fix the problem by iteslf, but it does have the integrated IAF so who knows.

The ONLY code stored was P0113, so replacing the MAF was the only option. The IAT is integral to the MAF on this 2000, according to Alldatdiy. Any thoughts on dielectric grease for the round external connector?