sounds like your glow plug relay!
i had the same problem with hard staring ,it was because my glow plugs were not working . the relay is on top of the engine next to the fuel filter. there are 2 of them 1 goes to the glow plugs . they cost $40 to $80 you can buy them on line or at napa. it...
MY F-250 SUPER DUTY 2000 MODEL NORMALLY STARTS UP FINE,BUT IF I DONT LET IT WARM UP 15 MINS. IT WILL STALL AND AFTER CRANKING AND PUMPING THE PEDEL IT WILL RESTART BUT UNLESS YOU LET IT WARM UP ,WILL STALL AGAIN .ONLY RUNS GOOD AFTER THE ENGINE IS WARM.TODAY IT WOULD NOT STAY RUNNING FOR MORE...