Hello. I hope the following is of assistance.
From the description you've given this will be a concern with the coolant temperature sensor. If the sensor becomes open circuit then the engine management uses a default value, usually around -40 degrees C, obviously when the engine is cold this isn't too much of a concern, when the engine becomes warm and is turned off when you try to start the car the engine management is still fueling for a cold engine so injects excessive fuel which in effect "floods" the engine which is when you get a non start.
Once the engine cools and you try to start it again as the engine management is fueling for a cold engine (albeit very cold) the engine will start again.
I hope this helps but if I can assist further let me know and I'll reply as soon as I'm able to.
So then just a replacement of the coolant temperature sensor? Any information on the part number I'd be looking for?
you can check the resistance through the sensor, if it's open circuit or has a high resistance then it will need replacing, the hotter the engine coolant the lower the resistance through the sensor becomes.
An idea of the sensor is at http://www.ebay.com/itm/Saab-93-95-96-11-Coolant-Temperature-Sensor-MEISTERSATZ-/350907499978?pt=Motors_Car_Truck_Parts_Accessories&hash=item51b3b785ca&vxp=mtr#vi-ilComp
but to be certain of the correct part you need to give the supplier the VIN of the car.
Let me know if I can assist further.