I asked if it had been tuned up recently because most likely the component causing the issue is one that would be replaced during a tune up. (As Cam mentioned) it is probably somewhere in coil to the plugs. When at operating temperature the wires or coil are probably breaking down and giving weak or no spark.
I also would say the fuel filter would be a good idea to change, that could be the problem and it never hurts to change it anyway (plus its pretty cheap and relatively easy)