Car will not start on 2003 Buick Rendezvous

Sometimes the car will not start after filling up with gas even tho I turn the gas tank lid several times. It has refused to start several times when it is hot. If I wait about 30 minutes it will than start. We have replaced the thermostat but it did not help.

You may have a problem with the anit-theft system. Is there a "security" light flashing when your Rendezvous won't start? There could also be fault codes stored in the engine or body computer which could help find the cause of you problem.
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Just helped a friend fix this exact same issue on his 2004 hyundai santa fe. Replaced the purge control valve - a $39 part, even from the dealer. Had to get our hands dirty, but it took literally one single hour to replace the part. Filled it up immediately afterward and no more starting problems. Part is located directly behind the manifold - top, rear of the engine compartment - just between the engine
I had this same problem on my Rendezvous. We checked fuses and the battery and it wasn't either of those. On vacation in North Carolina, we got stranded at a rest stop because the car wouldn't start. We called AAA and they sent out a tow truck. The car had been sitting for about an hour by the time the driver got there and he tried starting it, and it fired up right away! He said that because we topped off whenever we would fill up at the gas station, it was probably the fuel pump and it needed to be replaced.
do you "top off" you tank after the pump clicks? you might be saturating the EVAP canister. by letting it sit it evaporates and then starts. you can take it to autozone and ask them to pull the codes. if the EVAP canister or relay pops uo then it would confirm my suspision. my friend was having the same problme so it might be common for this vehicle.
We have to keep our 02 Rendezvous full of gas or it will fail to restart. Possibly due to fuel pump location in gas tank and pump overheats without gas covering.
yes seen you change the thermostart it refuse to started the main problem is change fuelpump fuel filter, service the nozzle and plugs.