Should I replace my Coil Pack to solve my hard starting issue when engine gets hot?

Hello, I have a 1999 Mercury Cougar with a 2.5L Duratec V6...has approx 170k miles on it. For the duration of time that I have owned the car, I have had problems starting the car after the engine gets hot. I have noticed that when cold (for the most part), the engine will only require a few cranks to get going. However, after periods of driving for 20-40 minutes, when I stop and turn the car off, and then attempt to restart, it will at times require excessive cranking to get the engine fired. At times, I have had to wait approx 15-20 minutes while letting the engine cool off before it would restart. I have checked my fuel pressure at the rail and the PSI numbers I am getting are up to spec (Cranking, While at Idle, under load, etc). I also recently changed my spark plugs and wires, all Motorcraft brand. After doing my own research, I have come across many opinions, but I keep hearing that a bad Coil pack displays many of the same symptoms that I am experiencing. In your best opinion, is this where I should start?

Thanks