Alan is probably on the right track in describing a fuel delivery issue (filters, sediment etc) (so long as that "Fire" is contained within a sealed cylinder then fire is good thing LOL )
It's VERY important to have a fuel filter between the gas tank and the fuel pump. Electric fuel pumps don't like dirt.
Other things to look at are the distributor, electrical connections and coil. All can produce a similar dilemma. If you have a point eliminator, they usually just fail completely but check the black and red leads that go to the coil. Coils can cause intermittent problems and when they cool off, they work and the car will start.
If you have points, check the gap and if the points are in good shape, replace the condenser and obviously if the points are bad then replace them also. There is a wire that energizes the coil with 12 volts when you switch on the key. They have been known to come loose completely or have corrosion that causes intermittent voltage to pass. Check inside the distributor cap for carbon arc's between each contact. If they are present then replace the cap and the rotor. Finally, I've seen cases where the tachometer had an intermittent short circuit and it caused the coil to ground out. When everything cooled down, it worked
In the big picture, it still sounds like a fuel delivery issue but it doesn't hurt to check out the complete system.