1989 GMC Vandura: starts fine from cold, fine from normal running temp, won't start when cooled down a little.?

I have a 1989 GMC Vandura which starts just fine from a cold engine. If the engine is warmed up to normal operating temperature, it will likewise start just fine. However, if I let the engine get to normal running temperature and then turn it off and leave it for, say, half an hour, it'll be very, very hard to start. When it does finally catch and start up, the idle speed will fluctuate quite a lot for 30 seconds to a minute or so. Where should I start my investigation?