If the check engine light is not on, could I still have fault codes and can they be read?

Check for spark when it does this. You could have to many ohms in teh crank or cam sensor and when it gets hot they lose sending power. Sometimes these will not set a code. Also recheck yoru fuel pressure when it does this.

Because you still lhave a distributor it could be a dist cap or a couple of bad wires. If you have an ohm meter, check wires for resistance if they have less than 5000 ohms per ft you are ok. Check the inside of the cap for thingsthat look like pencil lines, it could be shorting between two cylinders there. Also i'm including apic it could be the sensor inside your dist area or the igninition module as well. I think auto parst stores can test the lmodule for you.