The reason the engine was rebuilt by renault is because that is another Peugot/Renault/Volvo joint engines. What is the sevice history of this car has it had a tune up recently? If not, now is the time as moisture can cause problems. It sound like there is a problem with a bad connection caused by a small crack that forms when hot. Have you found out if there is spark and fuel? You must not have one of them as the car would otherwise start. I encountered a problem like this one and it turned out to be a bad computer. The car would not start when you tried to restart after about one to two hours. After that it would start and run fine. Turned out to be a crack or bad solder connection in the computer. When it was hot it was fine but sometime during the cooling off period it would loose it conection and then after it fully cooled off the connection would be made again.