Car wont start when warm. starts first time when cold. runs perfectly until stopped.starts if allowed to cool for 45 mins

I recommend replacing the fuel pump. I once experienced a similar situation with an Audi Quattro that was sensitive to temperature and would stop running when it was warm.

Think about what you just said. Only does this in times of higher temps out BUT never in winters cold. Doesn't that seem strange to you. Well I guess it does, huh. Anyway, know these systems helps. When engine is started, the temp sensor tells the computer it needs to place the engine to cold start mode. It does this and extra fuel is put into the cylinders to keep it running like a choke on the carbureted engines. But those you can turn the choke off or it does this automatically from the warmer engine. If in fact the temp sensor is not telling the computer it's warm enough to be taken out of cold start mode, it keeps dumping excessive fuel into the cylinders an flooding the engine causing it to surge and then die, because it's flooded. Therefore, the temperature sensor is faulty and needs replaced. Do that and drive on.

Check the water coolant thermostat. If it is stuck in the "open" position you are heating up all the water in the coolant system and this will take time. The thermostat keeps the water in the engine until warmed up to almost normal running temperature, only then does it allow the coolant to enter the radiator.

This could likely be a problem with your cooling, Next time you turn your car on pay attention to the temperature gauge and see if it rises above the norm.

Ok, time for car school. The vehicle is operated by the computer, every electrical concept that is. When the engine is cold, it starts fine because the computer has placed it in "cold start mode", putting more fuel into the engine than normally would until Once the engine is warmed up, a temperature sending unit or temp sensor tells the computer to change to normal run mode. IF said temp sensor is faulty and is not telling the computer to make said change, it stays in cold start mode, still dumping excess fuel in the engine that is now not required, cause it's warmed up. Like keeping the choke closed on older vehicles. Now I think you can answer your own question, when this no start action is happening after warm up and it always starts fine when cold, what's the first thing you check ? Right, the unsuspected temp sensor. Change that and no more start problem. Have a wonderful day. Glad I could be of service.

I would replace the coil. and condenser.

Most likely air flow metre. Had same problem analysed and replaced and runs perfectly. Not cheap!

I need to get a clear mental picture of what exactly is happening.

With this said, you stated that the car "runs fine" until warmed up.

Q: When you start the car when cold it idles fine?
Q: If you allow the car to idle until "fully" warmed does the car stall?
Q: As the car begins to warm up, Does the RPM fluctuate abnormally?
Q: Does the car Only stall when you press on the gas pedal or does it stall just sitting and idling in addition to pressing the gas pedal?
Q: If you can drive it while cold does the car stall during acceleration when warm or only at Stop Signs / Lights?
Q: If you wait 20min or so, can you start the car again?
Q: How many miles are on the car?

need more info when it dosnt start what does it do? if it cranks may be sensor or relay like fuel pump relay ect.

take it to a volvo dealer and have the codes read
most likely a coolant temp sensor, ambient temp sensor, Baro sensor, MAP/VAF sensor problem the fault codes will tell you