My 5.0 wont run in the heat

I've got a 1987 5.0 that wont run when it's hot outside.  It will run fine at first but slowly looses fuel pressure and dies.  I've taken it to several mechanics including my local Ford dealer.  The first mechanic insisted it was the fuel pump so a new one was put in.  The problem didnt go away.  Ford dealer suggested doing the same thing but not 100% sure.  Not wanting to put another fuel pump in just for fun I'm stuck on what to do.  My mustang has the following mods: roller rockers, BBK adjustable fuel pressure regulator, bigger than stock throttle body (not sure what size), cool air intake (inner fender type), MAC shortie headers, MSD ingnition.  Any ideas anybody has will be greatly appreciated.  

there is a sock in the fuel tank at the bottom of the fuel sending unit.It gets clogged while the engine is running and starves the vehile as the car runs<<<then when shut off the sediment on the sock falls off in the tank till the car is run again and sediment gets sucked up into clogging the sock again........  

Thanks for your reply but your solution doesn't answer my temperature problem.  The car ran fine all winter and early spring.  The outside temperature hasn't gotten above 70.  This last week it was 80 degrees.  I drove the same 30 mile trip I've been running several times a week for the last few months and suddenly after about 20 min. the car begins to feel like its starved for fuel and dies when I take the car out of gear.  After letting the car cool down it starts up again.  The fuel pressure is low and it steadly drops until the engine dies again.