My Focus hesitates and loses power and has engine code on.

My 2007 Focus hesitated and lost power, then produced engine code. Shutting off engine for 5-10 minutes allows me to start and drive again. I took it in to a mechanic, who ran the diagnoses, which indicated fuel filter and possibly fuel pump as the cause. He replaced the fuel filter and we set appt. To replace fuel pump. Meanwhile, we drove vehicle for two weeks without further symptoms occurring, so decided not to replace the spendy in-tank fuel pump. The outside temperatures were in the high 90's at the first occurrence, but there was no heat guage change or coolant loss.
After 4 weeks, the car did the same thing again, again on an 89 degree day with air conditioning and cruise control on. Stopping for a few minutes restored power and cooler weather seems to eliminate the problem.

Could the problem be the fuel pump, when it works fine all but in heat situations?

Could there be a plugged air intake/air filter, or a sensor that would cause problems only during hot weather with engine under "load"?